Glossary of Riemannian and metric geometry (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Glossary of Riemannian and metric geometry" in English language version.

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doi.org

Mancinelli, Claudio; Puppo, Enrico (2023-06-01). "Computing the Riemannian center of mass on meshes". Computer Aided Geometric Design. 103: 102203. doi:10.1016/j.cagd.2023.102203. ISSN 0167-8396.
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004), Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (eds.), "Riemannian metrics", Riemannian Geometry, Berlin, Heidelberg: Springer, Remark after Proof of Corollary 2.89, p.87, doi:10.1007/978-3-642-18855-8_2, ISBN 978-3-642-18855-8, retrieved 2024-11-28
Petersen, Peter (2016), Petersen, Peter (ed.), "Sectional Curvature Comparison I", Riemannian Geometry, Graduate Texts in Mathematics, vol. 171, Cham: Springer International Publishing, Theorem 6.4.8, pp. 258-259, doi:10.1007/978-3-319-26654-1_6, ISBN 978-3-319-26654-1, retrieved 2024-11-29
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004), Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (eds.), "Curvature", Riemannian Geometry, Berlin, Heidelberg: Springer, Scholium 3.78, doi:10.1007/978-3-642-18855-8_3, ISBN 978-3-642-18855-8, retrieved 2024-11-28
Hirsch, Morris W. (1970). "Expanding maps and transformation groups". Global Analysis. Proceedings of Symposia in Pure Mathematics. Vol. 14. pp. 125–131. doi:10.1090/pspum/014/0298701. ISBN 978-0-8218-1414-7. Zbl 0223.58009.
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "δ-Hyperbolic Spaces and Area", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, 2. Area and isoperimetric inequalities, pp. 414 – 417, doi:10.1007/978-3-662-12494-9_21, ISBN 978-3-662-12494-9, retrieved 2024-12-23
Lang, Serge (1999). "Fundamentals of Differential Geometry". Graduate Texts in Mathematics. 191. Chapter XII An example of seminegative curvature, p. 323. doi:10.1007/978-1-4612-0541-8. ISBN 978-1-4612-6810-9. ISSN 0072-5285.
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "Basic Concepts", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, Chapter I.1, § Metric spaces, Definitions 1.1, p. 2, doi:10.1007/978-3-662-12494-9_1, ISBN 978-3-662-12494-9, retrieved 2024-11-29
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "Non-Positive Curvature and Group Theory", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, Definition 3.4, p. 460, doi:10.1007/978-3-662-12494-9_22, ISBN 978-3-662-12494-9, retrieved 2024-12-23
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 7, §7.3.1 Rays and Lines, p. 298. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Berestovskii, V. N. (1987-07-01). "Submetries of space-forms of negative curvature". Siberian Mathematical Journal. 28 (4): 552–562. Bibcode:1987SibMJ..28..552B. doi:10.1007/BF00973842. ISSN 1573-9260.
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 12, §12.4 The Soul Theorem, p. 463. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). "Riemannian Geometry". Universitext. Chapter 2, §2.C.1, Definition 2.80 bis, p.82. doi:10.1007/978-3-642-18855-8. ISBN 978-3-540-20493-0. ISSN 0172-5939.

harvard.edu

ui.adsabs.harvard.edu

Berestovskii, V. N. (1987-07-01). "Submetries of space-forms of negative curvature". Siberian Mathematical Journal. 28 (4): 552–562. Bibcode:1987SibMJ..28..552B. doi:10.1007/BF00973842. ISSN 1573-9260.

springer.com

link.springer.com

Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004), Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (eds.), "Riemannian metrics", Riemannian Geometry, Berlin, Heidelberg: Springer, Remark after Proof of Corollary 2.89, p.87, doi:10.1007/978-3-642-18855-8_2, ISBN 978-3-642-18855-8, retrieved 2024-11-28
Petersen, Peter (2016), Petersen, Peter (ed.), "Sectional Curvature Comparison I", Riemannian Geometry, Graduate Texts in Mathematics, vol. 171, Cham: Springer International Publishing, Theorem 6.4.8, pp. 258-259, doi:10.1007/978-3-319-26654-1_6, ISBN 978-3-319-26654-1, retrieved 2024-11-29
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004), Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (eds.), "Curvature", Riemannian Geometry, Berlin, Heidelberg: Springer, Scholium 3.78, doi:10.1007/978-3-642-18855-8_3, ISBN 978-3-642-18855-8, retrieved 2024-11-28
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "δ-Hyperbolic Spaces and Area", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, 2. Area and isoperimetric inequalities, pp. 414 – 417, doi:10.1007/978-3-662-12494-9_21, ISBN 978-3-662-12494-9, retrieved 2024-12-23
Lang, Serge (1999). "Fundamentals of Differential Geometry". Graduate Texts in Mathematics. 191. Chapter XII An example of seminegative curvature, p. 323. doi:10.1007/978-1-4612-0541-8. ISBN 978-1-4612-6810-9. ISSN 0072-5285.
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "Basic Concepts", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, Chapter I.1, § Metric spaces, Definitions 1.1, p. 2, doi:10.1007/978-3-662-12494-9_1, ISBN 978-3-662-12494-9, retrieved 2024-11-29
Bridson, Martin R.; Haefliger, André (1999), Bridson, Martin R.; Haefliger, André (eds.), "Non-Positive Curvature and Group Theory", Metric Spaces of Non-Positive Curvature, Berlin, Heidelberg: Springer, Definition 3.4, p. 460, doi:10.1007/978-3-662-12494-9_22, ISBN 978-3-662-12494-9, retrieved 2024-12-23
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 7, §7.3.1 Rays and Lines, p. 298. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Berestovskii, V. N. (1987-07-01). "Submetries of space-forms of negative curvature". Siberian Mathematical Journal. 28 (4): 552–562. Bibcode:1987SibMJ..28..552B. doi:10.1007/BF00973842. ISSN 1573-9260.
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 12, §12.4 The Soul Theorem, p. 463. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). "Riemannian Geometry". Universitext. Chapter 2, §2.C.1, Definition 2.80 bis, p.82. doi:10.1007/978-3-642-18855-8. ISBN 978-3-540-20493-0. ISSN 0172-5939.

worldcat.org

search.worldcat.org

Mancinelli, Claudio; Puppo, Enrico (2023-06-01). "Computing the Riemannian center of mass on meshes". Computer Aided Geometric Design. 103: 102203. doi:10.1016/j.cagd.2023.102203. ISSN 0167-8396.
Lang, Serge (1999). "Fundamentals of Differential Geometry". Graduate Texts in Mathematics. 191. Chapter XII An example of seminegative curvature, p. 323. doi:10.1007/978-1-4612-0541-8. ISBN 978-1-4612-6810-9. ISSN 0072-5285.
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 7, §7.3.1 Rays and Lines, p. 298. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Berestovskii, V. N. (1987-07-01). "Submetries of space-forms of negative curvature". Siberian Mathematical Journal. 28 (4): 552–562. Bibcode:1987SibMJ..28..552B. doi:10.1007/BF00973842. ISSN 1573-9260.
Petersen, Peter (2016). "Riemannian Geometry". Graduate Texts in Mathematics. 171. Chapter 12, §12.4 The Soul Theorem, p. 463. doi:10.1007/978-3-319-26654-1. ISBN 978-3-319-26652-7. ISSN 0072-5285.
Gallot, Sylvestre; Hulin, Dominique; Lafontaine, Jacques (2004). "Riemannian Geometry". Universitext. Chapter 2, §2.C.1, Definition 2.80 bis, p.82. doi:10.1007/978-3-642-18855-8. ISBN 978-3-540-20493-0. ISSN 0172-5939.

zbmath.org

Kobayashi, Shōshichi; Nomizu, Katsumi (1963). "Chapter VII Submanifolds, 8. Autoparallel submanifolds and totally geodesic submanifolds". Foundations of differential geometry. Interscience Publishers, New York, NY. pp. 53–62. ISBN 978-0-471-15732-8. Zbl 0175.48504.
Lee, Jeffrey M. (2009). "13. Riemannian and Semi-Riemannian Geometry, Definition 13.141". Manifolds and differential geometry. Providence, RI: American Mathematical Society (AMS). p. 615. ISBN 978-0-8218-4815-9. Zbl 1190.58001.
Hirsch, Morris W. (1970). "Expanding maps and transformation groups". Global Analysis. Proceedings of Symposia in Pure Mathematics. Vol. 14. pp. 125–131. doi:10.1090/pspum/014/0298701. ISBN 978-0-8218-1414-7. Zbl 0223.58009.
Burago, Dmitri; Burago, Yurii; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society (AMS). Chapter 7, §7.2, pp. 249-250. ISBN 0-8218-2129-6. Zbl 0981.51016.
Burago, Dmitri; Burago, Yurii; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society (AMS). Chapter 9, §9.1, pp. 321-322. ISBN 0-8218-2129-6. Zbl 0981.51016.
Burago, Dmitri; Burago, Yurii; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society (AMS). Chapter 2, §2.5.1, Definition 2.5.7. ISBN 0-8218-2129-6. Zbl 0981.51016.
Burago, Dmitri; Burago, Yurii; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society (AMS). Chapter 1, §1.6, Definition 1.6.1, p. 13. ISBN 0-8218-2129-6. Zbl 0981.51016.
Burago, Dmitri; Burago, Yurii; Ivanov, Sergei (2001). A course in metric geometry. Providence, RI: American Mathematical Society (AMS). Chapter 10, §10.4, Exercise 10.4.5, p. 366. ISBN 0-8218-2129-6. Zbl 0981.51016.