Bochner's theorem (Riemannian geometry) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Bochner's theorem (Riemannian geometry)" in English language version.

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Kobayashi & Nomizu 1963, Corollary VI.5.4; Petersen 2016, Corollary 8.2.3. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Kobayashi 1972. Kobayashi, Shoshichi (1972). "Isometries of Riemannian Manifolds". Transformation groups in differential geometry (PDF). Ergebnisse der Mathematik und ihrer Grenzgebiete. Vol. 70. Springer-Verlag. pp. 55−57. ISBN 9780387058481. MR 0355886.
Wu 2017. Wu, Hung-Hsi (2017). The Bochner technique in differential geometry. Classical Topics in Mathematics. Vol. 6 (New expanded ed.). Beijing: Higher Education Press. pp. 30–32. ISBN 978-7-04-047838-9. MR 3838345.
Kobayashi & Nomizu 1963, Theorem VI.3.4; Petersen 2016, p. 316. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Kobayashi & Nomizu 1963, Theorem VI.3.4. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help)
Taylor 2011, p. 305. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.
Petersen 2016, Proposition 8.2.1. 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.
Kobayashi & Nomizu 1963, Theorem 5.3; Petersen 2016, Theorem 8.2.2; Taylor 2011, p. 305. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.

doi.org

Kobayashi & Nomizu 1963, Corollary VI.5.4; Petersen 2016, Corollary 8.2.3. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Kobayashi & Nomizu 1963, Theorem VI.3.4; Petersen 2016, p. 316. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Taylor 2011, p. 305. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.
Petersen 2016, Proposition 8.2.1. 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.
Kobayashi & Nomizu 1963, Theorem 5.3; Petersen 2016, Theorem 8.2.2; Taylor 2011, p. 305. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.

ed.ac.uk

empg.maths.ed.ac.uk

Kobayashi 1972. Kobayashi, Shoshichi (1972). "Isometries of Riemannian Manifolds". Transformation groups in differential geometry (PDF). Ergebnisse der Mathematik und ihrer Grenzgebiete. Vol. 70. Springer-Verlag. pp. 55−57. ISBN 9780387058481. MR 0355886.

zbmath.org

Kobayashi & Nomizu 1963, Corollary VI.5.4; Petersen 2016, Corollary 8.2.3. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Kobayashi & Nomizu 1963, Theorem VI.3.4; Petersen 2016, p. 316. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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.
Kobayashi & Nomizu 1963, Theorem VI.3.4. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help)
Taylor 2011, p. 305. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.
Petersen 2016, Proposition 8.2.1. 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.
Kobayashi & Nomizu 1963, Theorem 5.3; Petersen 2016, Theorem 8.2.2; Taylor 2011, p. 305. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol. 15. Reprinted in 1996. New York–London: John Wiley & Sons, Inc. ISBN 0-471-15733-3. MR 0152974. Zbl 0119.37502. {{cite book}}: ISBN / Date incompatibility (help) 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. Taylor, Michael E. (2011). Partial differential equations II. Qualitative studies of linear equations. Applied Mathematical Sciences. Vol. 116 (Second edition of 1996 original ed.). New York: Springer. doi:10.1007/978-1-4419-7052-7. ISBN 978-1-4419-7051-0. MR 2743652. Zbl 1206.35003.