Scalar curvature (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Scalar curvature" in English language version.

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Gallot, Hulin & Lafontaine 2004, Definition 3.19; Lawson & Michelsohn 1989, p. 160; Petersen 2016, Section 1.5.2. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Aubin 1998, Section 1.2.3; Petersen 2016, Section 1.5.2. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, Definition 3.19; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Petersen 2016, Section 3.1.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 1F; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Bao, Chern & Shen 2000. Bao, D.; Chern, S.-S.; Shen, Z. (2000). An introduction to Riemann–Finsler geometry. Graduate Texts in Mathematics. Vol. 200. New York: Springer-Verlag. doi:10.1007/978-1-4612-1268-3. ISBN 0-387-98948-X. MR 1747675. Zbl 0954.53001.
Aubin 1998, Definition 1.22; Jost 2017, p. 200; Petersen 2016, Remark 3.1.7. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, p. 135; Petersen 2016, p. 30. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Lawson & Michelsohn 1989, p. 160. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
do Carmo 1992, Section 4.4. do Carmo, Manfredo Perdigão (1992). Riemannian geometry. Mathematics: Theory & Applications. Translated from the second Portuguese edition by Francis Flaherty. Boston, MA: Birkhäuser Boston, Inc. ISBN 0-8176-3490-8. MR 1138207. Zbl 0752.53001.
Berline, Getzler & Vergne 2004, p. 34. Berline, Nicole; Getzler, Ezra; Vergne, Michèle (2004). Heat kernels and Dirac operators. Grundlehren Text Editions (Corrected reprint of the 1992 original ed.). Berlin: Springer-Verlag. doi:10.1007/978-3-642-58088-8. ISBN 978-3-540-20062-8. MR 2273508. Zbl 1037.58015.
Besse 1987, p. 10; Gallot, Hulin & Lafontaine 2004, p. 135; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, p. 144. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
do Carmo 1992, pp. 107–108. do Carmo, Manfredo Perdigão (1992). Riemannian geometry. Mathematics: Theory & Applications. Translated from the second Portuguese edition by Francis Flaherty. Boston, MA: Birkhäuser Boston, Inc. ISBN 0-8176-3490-8. MR 1138207. Zbl 0752.53001.
O'Neill 1983, pp. 90–91. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
O'Neill 1983, p. 92. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, Example 2.4.3. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
Aubin 1998, Section 1.2.3; Gallot, Hulin & Lafontaine 2004, Section 3.K.3; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 3C; O'Neill 1983, p. 336. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Besse 1987, Sections 1G and 1H. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 2D. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Aubin 1998, p. 146; Besse 1987, Section 1J. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 1K. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Chavel 1984, Section XII.8; Gallot, Hulin & Lafontaine 2004, Section 3.H.4. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001.
Chavel 1984, Section XII.8. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001.
O'Neill 1983, p. 345. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Petersen 2016, Section 4.2.3. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Lee & Parker 1987. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/S0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Besse 1987, Section 1I; Gilkey 1995, Section 4.1; Jost 2017, Sections 4.4 and 4.5; Lawson & Michelsohn 1989, Section II.8. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Lawson & Michelsohn 1989, Sections II.8 and IV.3. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.3; Lawson & Michelsohn 1989, Section IV.5. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.4. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054.
Jost 2017, Section 11.2. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001.
Perelman 2003, Section 6.1; Cao & Zhu 2006, Corollary 7.4.4; Kleiner & Lott 2008, Lemmas 81.1 and 81.2. Perelman, Grisha (March 2003). "Ricci flow with surgery on three-manifolds". arXiv:math/0303109. Kleiner, Bruce; Lott, John (2008). "Notes on Perelman's papers". Geometry & Topology. 12 (5). Updated for corrections in 2011 & 2013: 2587–2855. arXiv:math/0605667. doi:10.2140/gt.2008.12.2587. MR 2460872. Zbl 1204.53033.
Lawson & Michelsohn 1989, Section IV.4. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Berger 2003, Section 12.3.3. Berger, Marcel (2003). A panoramic view of Riemannian geometry. Berlin: Springer-Verlag. doi:10.1007/978-3-642-18245-7. ISBN 3-540-65317-1. MR 2002701. Zbl 1038.53002.
Besse 1987, Theorem 4.35. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Petersen 2016, Corollary C.4.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.

arxiv.org

Perelman 2003, Section 6.1; Cao & Zhu 2006, Corollary 7.4.4; Kleiner & Lott 2008, Lemmas 81.1 and 81.2. Perelman, Grisha (March 2003). "Ricci flow with surgery on three-manifolds". arXiv:math/0303109. Kleiner, Bruce; Lott, John (2008). "Notes on Perelman's papers". Geometry & Topology. 12 (5). Updated for corrections in 2011 & 2013: 2587–2855. arXiv:math/0605667. doi:10.2140/gt.2008.12.2587. MR 2460872. Zbl 1204.53033.

doi.org

Gallot, Hulin & Lafontaine 2004, Definition 3.19; Lawson & Michelsohn 1989, p. 160; Petersen 2016, Section 1.5.2. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Aubin 1998, Section 1.2.3; Petersen 2016, Section 1.5.2. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, Definition 3.19; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Petersen 2016, Section 3.1.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 1F; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Bao, Chern & Shen 2000. Bao, D.; Chern, S.-S.; Shen, Z. (2000). An introduction to Riemann–Finsler geometry. Graduate Texts in Mathematics. Vol. 200. New York: Springer-Verlag. doi:10.1007/978-1-4612-1268-3. ISBN 0-387-98948-X. MR 1747675. Zbl 0954.53001.
Aubin 1998, Definition 1.22; Jost 2017, p. 200; Petersen 2016, Remark 3.1.7. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, p. 135; Petersen 2016, p. 30. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Berline, Getzler & Vergne 2004, p. 34. Berline, Nicole; Getzler, Ezra; Vergne, Michèle (2004). Heat kernels and Dirac operators. Grundlehren Text Editions (Corrected reprint of the 1992 original ed.). Berlin: Springer-Verlag. doi:10.1007/978-3-642-58088-8. ISBN 978-3-540-20062-8. MR 2273508. Zbl 1037.58015.
Besse 1987, p. 10; Gallot, Hulin & Lafontaine 2004, p. 135; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, p. 144. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
O'Neill 1983, pp. 90–91. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
O'Neill 1983, p. 92. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, Example 2.4.3. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
Aubin 1998, Section 1.2.3; Gallot, Hulin & Lafontaine 2004, Section 3.K.3; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 3C; O'Neill 1983, p. 336. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Besse 1987, Sections 1G and 1H. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 2D. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Aubin 1998, p. 146; Besse 1987, Section 1J. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 1K. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Chavel 1984, Section XII.8; Gallot, Hulin & Lafontaine 2004, Section 3.H.4. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001.
Chavel 1984, Section XII.8. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001.
O'Neill 1983, p. 345. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Petersen 2016, Section 4.2.3. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Lee & Parker 1987. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/S0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Besse 1987, Section 1I; Gilkey 1995, Section 4.1; Jost 2017, Sections 4.4 and 4.5; Lawson & Michelsohn 1989, Section II.8. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.3; Lawson & Michelsohn 1989, Section IV.5. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.4. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054.
Jost 2017, Section 11.2. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001.
Perelman 2003, Section 6.1; Cao & Zhu 2006, Corollary 7.4.4; Kleiner & Lott 2008, Lemmas 81.1 and 81.2. Perelman, Grisha (March 2003). "Ricci flow with surgery on three-manifolds". arXiv:math/0303109. Kleiner, Bruce; Lott, John (2008). "Notes on Perelman's papers". Geometry & Topology. 12 (5). Updated for corrections in 2011 & 2013: 2587–2855. arXiv:math/0605667. doi:10.2140/gt.2008.12.2587. MR 2460872. Zbl 1204.53033.
Berger 2003, Section 12.3.3. Berger, Marcel (2003). A panoramic view of Riemannian geometry. Berlin: Springer-Verlag. doi:10.1007/978-3-642-18245-7. ISBN 3-540-65317-1. MR 2002701. Zbl 1038.53002.
Besse 1987, Theorem 4.35. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Petersen 2016, Corollary C.4.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.

zbmath.org

Gallot, Hulin & Lafontaine 2004, Definition 3.19; Lawson & Michelsohn 1989, p. 160; Petersen 2016, Section 1.5.2. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Aubin 1998, Section 1.2.3; Petersen 2016, Section 1.5.2. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, Definition 3.19; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Petersen 2016, Section 3.1.5. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 1F; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Bao, Chern & Shen 2000. Bao, D.; Chern, S.-S.; Shen, Z. (2000). An introduction to Riemann–Finsler geometry. Graduate Texts in Mathematics. Vol. 200. New York: Springer-Verlag. doi:10.1007/978-1-4612-1268-3. ISBN 0-387-98948-X. MR 1747675. Zbl 0954.53001.
Aubin 1998, Definition 1.22; Jost 2017, p. 200; Petersen 2016, Remark 3.1.7. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Gallot, Hulin & Lafontaine 2004, p. 135; Petersen 2016, p. 30. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Lawson & Michelsohn 1989, p. 160. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
do Carmo 1992, Section 4.4. do Carmo, Manfredo Perdigão (1992). Riemannian geometry. Mathematics: Theory & Applications. Translated from the second Portuguese edition by Francis Flaherty. Boston, MA: Birkhäuser Boston, Inc. ISBN 0-8176-3490-8. MR 1138207. Zbl 0752.53001.
Berline, Getzler & Vergne 2004, p. 34. Berline, Nicole; Getzler, Ezra; Vergne, Michèle (2004). Heat kernels and Dirac operators. Grundlehren Text Editions (Corrected reprint of the 1992 original ed.). Berlin: Springer-Verlag. doi:10.1007/978-3-642-58088-8. ISBN 978-3-540-20062-8. MR 2273508. Zbl 1037.58015.
Besse 1987, p. 10; Gallot, Hulin & Lafontaine 2004, p. 135; O'Neill 1983, p. 88. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, p. 144. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
do Carmo 1992, pp. 107–108. do Carmo, Manfredo Perdigão (1992). Riemannian geometry. Mathematics: Theory & Applications. Translated from the second Portuguese edition by Francis Flaherty. Boston, MA: Birkhäuser Boston, Inc. ISBN 0-8176-3490-8. MR 1138207. Zbl 0752.53001.
O'Neill 1983, pp. 90–91. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
O'Neill 1983, p. 92. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Gilkey 1995, Example 2.4.3. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001.
Aubin 1998, Section 1.2.3; Gallot, Hulin & Lafontaine 2004, Section 3.K.3; Petersen 2016, Section 3.1.5. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Besse 1987, Section 3C; O'Neill 1983, p. 336. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Besse 1987, Sections 1G and 1H. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 2D. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Aubin 1998, p. 146; Besse 1987, Section 1J. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Besse 1987, Section 1K. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Chavel 1984, Section XII.8; Gallot, Hulin & Lafontaine 2004, Section 3.H.4. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001. Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). Riemannian geometry. Universitext (Third ed.). Springer-Verlag. doi:10.1007/978-3-642-18855-8. ISBN 3-540-20493-8. MR 2088027. Zbl 1068.53001.
Chavel 1984, Section XII.8. Chavel, Isaac (1984). Eigenvalues in Riemannian geometry. Pure and Applied Mathematics. Vol. 115. Orlando, FL: Academic Press. doi:10.1016/s0079-8169(08)x6051-9. ISBN 0-12-170640-0. MR 0768584. Zbl 0551.53001.
O'Neill 1983, p. 345. O'Neill, Barrett (1983). Semi-Riemannian geometry. With applications to relativity. Pure and Applied Mathematics. Vol. 103. New York: Academic Press, Inc. doi:10.1016/s0079-8169(08)x6002-7. ISBN 0-12-526740-1. MR 0719023. Zbl 0531.53051.
Petersen 2016, Section 4.2.3. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.
Lee & Parker 1987. Lee, John M.; Parker, Thomas H. (1987). "The Yamabe problem". Bulletin of the American Mathematical Society. New Series. 17 (1): 37–91. doi:10.1090/S0273-0979-1987-15514-5. MR 0888880. Zbl 0633.53062.
Besse 1987, Section 1I; Gilkey 1995, Section 4.1; Jost 2017, Sections 4.4 and 4.5; Lawson & Michelsohn 1989, Section II.8. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001. Gilkey, Peter B. (1995). Invariance theory, the heat equation, and the Atiyah–Singer index theorem. Studies in Advanced Mathematics (Second edition of 1984 original ed.). Boca Raton, FL: CRC Press. doi:10.1201/9780203749791. ISBN 0-8493-7874-5. MR 1396308. Zbl 0856.58001. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Lawson & Michelsohn 1989, Sections II.8 and IV.3. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.3; Lawson & Michelsohn 1989, Section IV.5. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Blackadar 1998, Section 24.4. Blackadar, Bruce (1998). K-theory for operator algebras. Mathematical Sciences Research Institute Publications. Vol. 5 (Second edition of 1986 original ed.). Cambridge: Cambridge University Press. doi:10.1007/978-1-4613-9572-0. ISBN 0-521-63532-2. MR 1656031. Zbl 0913.46054.
Jost 2017, Section 11.2. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Springer, Cham. doi:10.1007/978-3-319-61860-9. ISBN 978-3-319-61859-3. MR 3726907. Zbl 1380.53001.
Perelman 2003, Section 6.1; Cao & Zhu 2006, Corollary 7.4.4; Kleiner & Lott 2008, Lemmas 81.1 and 81.2. Perelman, Grisha (March 2003). "Ricci flow with surgery on three-manifolds". arXiv:math/0303109. Kleiner, Bruce; Lott, John (2008). "Notes on Perelman's papers". Geometry & Topology. 12 (5). Updated for corrections in 2011 & 2013: 2587–2855. arXiv:math/0605667. doi:10.2140/gt.2008.12.2587. MR 2460872. Zbl 1204.53033.
Lawson & Michelsohn 1989, Section IV.4. Lawson, H. Blaine Jr.; Michelsohn, Marie-Louise (1989). Spin geometry. Princeton Mathematical Series. Vol. 38. Princeton, NJ: Princeton University Press. ISBN 0-691-08542-0. MR 1031992. Zbl 0688.57001.
Berger 2003, Section 12.3.3. Berger, Marcel (2003). A panoramic view of Riemannian geometry. Berlin: Springer-Verlag. doi:10.1007/978-3-642-18245-7. ISBN 3-540-65317-1. MR 2002701. Zbl 1038.53002.
Besse 1987, Theorem 4.35. Besse, Arthur L. (1987). Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Vol. 10. Reprinted in 2008. Berlin: Springer-Verlag. doi:10.1007/978-3-540-74311-8. ISBN 3-540-15279-2. MR 0867684. Zbl 0613.53001.
Petersen 2016, Corollary C.4.4. Petersen, Peter (2016). Riemannian geometry. Graduate Texts in Mathematics. Vol. 171 (Third edition of 1998 original ed.). Springer, Cham. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. MR 3469435. Zbl 1417.53001.