Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu...
7 KB (675 words) - 22:07, 7 July 2025
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to...
76 KB (10,907 words) - 15:23, 21 July 2025
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...
129 KB (17,641 words) - 04:23, 28 July 2025
Kobayashi at the University of California, Berkeley, resulting in the classic two-volume work, Foundations of Differential Geometry in 1963. A second volume...
7 KB (867 words) - 03:32, 28 March 2025
intersection of algebraic geometry, differential geometry, and complex analysis, and uses tools from all three areas. Because of the blend of techniques...
26 KB (3,677 words) - 14:31, 7 September 2023
Shoshichi Kobayashi (category Differential geometers)
retirement under the VERIP plan in 1994. The two-volume book Foundations of Differential Geometry, which he coauthored with Katsumi Nomizu, has been known...
15 KB (1,585 words) - 08:54, 25 May 2025
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds....
46 KB (5,964 words) - 05:02, 17 July 2025
This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following...
28 KB (3,756 words) - 15:15, 3 July 2025
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...
11 KB (1,395 words) - 21:40, 22 July 2025
MR 1834454. Kobayashi, Shoshichi; Nomizu, Katsumi (1996), Foundations of Differential Geometry, vol. 1 (New ed.), Wiley-Interscience, ISBN 0-471-15733-3...
9 KB (1,295 words) - 22:19, 25 November 2024
Oswald Veblen (category University of Iowa alumni)
edn. 1931) Invariants of Quadratic Differential Forms (Cambridge University Press, 1927) The Foundations of Differential Geometry with J. H. C. Whitehead...
14 KB (1,236 words) - 18:05, 30 July 2025
Cartan connection (redirect from Cartan geometry)
In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also...
46 KB (6,755 words) - 22:53, 22 July 2024
Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It...
10 KB (1,015 words) - 01:11, 20 June 2025
mechanism (using precomposition) turns several constructions in differential geometry into contravariant functors. Let ϕ : M → N {\displaystyle \phi :M\to...
13 KB (2,251 words) - 10:33, 30 October 2024
Nash embedding theorems (redirect from Nash theorems (in differential geometry))
2022-05-06. Kobayashi, Shoshichi; Nomizu, Katsumi (1969). Foundations of differential geometry. Vol II. Interscience Tracts in Pure and Applied Mathematics...
17 KB (1,970 words) - 22:57, 5 August 2025
Synthetic differential geometry is an application of topos theory to the foundations of differentiable manifold theory. Foundations of geometry Incidence...
14 KB (1,712 words) - 23:39, 19 June 2025
theory of surfaces, and introduced the idea of principal curvatures, laying the foundation for subsequent developments in the differential geometry of surfaces...
97 KB (10,426 words) - 05:22, 15 July 2025
(as described in Ch XI of Kobayashi and Nomizu, Foundations of Differential Geometry Vol II.). A Chern connection, a connection of a holomorphic vector...
583 bytes (104 words) - 02:14, 8 December 2020
Embedding (category Differential topology)
ISBN 978-0-387-98593-0. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of Differential Geometry, Volume 1. New York: Wiley-Interscience. Lee, John Marshall...
18 KB (2,687 words) - 17:10, 20 March 2025
Curvature form (redirect from Differential Bianchi identity)
In differential geometry, the curvature form describes curvature of a connection on a principal bundle. The Riemann curvature tensor in Riemannian geometry...
5 KB (884 words) - 23:37, 25 February 2025
ISBN 0-691-07239-6. Dillen, F. J. E.; Verstraelen, L.C.A. (2000). Handbook of Differential Geometry. Vol. 1. Amsterdam: North-Holland. ISBN 0-444-82240-2. Pfister...
4 KB (601 words) - 10:00, 15 February 2025
Zbl 1380.53001. Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. New York–London: John Wiley & Sons, Inc. MR 0152974...
14 KB (2,103 words) - 17:25, 3 August 2025
Geodesic (category Differential geometry)
section 1.4. Kobayashi, Shoshichi; Nomizu, Katsumi (1996), Foundations of Differential Geometry, vol. 1 (New ed.), Wiley-Interscience, ISBN 0-471-15733-3...
32 KB (4,304 words) - 17:43, 5 July 2025
doi:10.1007/BF01236917. S. Kobayashi & K. Nomizu (1963). Foundations of differential geometry. Vol. I. Interscience. p. 166. Joshi, K. D. (1983). "Chapter...
13 KB (1,906 words) - 15:30, 12 September 2024
Kobayashi, S.; Nomizu, K. (2009) [1969]. "Appendix 8". Foundations of Differential Geometry. Wiley Classics Library. Vol. 2. Wiley. ISBN 978-0-471-15732-8...
28 KB (4,231 words) - 12:44, 26 May 2025
Cartan–Hadamard theorem (category Metric geometry)
ISBN 0-8176-3490-8. Kobayashi, Shoshichi; Nomizu, Katsumi (1969), Foundations of Differential Geometry, Vol. II, Tracts in Mathematics 15, New York: Wiley Interscience...
8 KB (968 words) - 01:48, 3 March 2023
Homogeneous space (section Geometry)
sense of isometry (rigid geometry), diffeomorphism (differential geometry), or homeomorphism (topology). Some authors insist that the action of G be faithful...
15 KB (1,826 words) - 14:59, 9 July 2025
Kobayashi, Shoshichi; Nomizu, Katsumi (1963). Foundations of differential geometry. Vol I. Interscience Tracts in Pure and Applied Mathematics. Vol...
6 KB (787 words) - 09:10, 19 April 2022
Ricci curvature (category Differential geometry)
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object that is determined by a choice of Riemannian...
34 KB (5,807 words) - 18:25, 6 August 2025
Jacobi field (redirect from Jacobi differential equation)
ISBN 978-0-8218-4417-5 Shoshichi Kobayashi and Katsumi Nomizu. Foundations of differential geometry. Vol. II. Reprint of the 1969 original. Wiley Classics Library. A Wiley-Interscience...
7 KB (1,433 words) - 06:22, 16 May 2025