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- Foundations_of_Differential_Geometry abstract "Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.The first volume considers manifolds, fiber bundles, tensor analysis, connections in bundles, and the role of Lie groups. It also covers holonomy, the de Rham decomposition theorem and the Hopf-Rinow theorem. According to the review of J. Eells, it has a "fine expositional style" and consists of a "special blend of algebraic, analytic, and geometric concepts". Eells says it is "essentially a textbook (even though there are no exercises)". An advanced text, it has a "pace geared to a [one] term graduate course".The second volume considers submanifolds of Riemannian manifolds, the Gauss map, and the second fundamental form. It continues with geodesics on Riemannian manifolds, the Jacobi field, Morse index, the Rauch comparison theorems and the Cartan-Hadamard theorem. Then it ascends to complex manifolds, Kahlerian manifolds, homogeneous spaces, and symmetric spaces. In a discussion of curvature representation of characteristic classes of principal bundles (Chern–Weil theory), it covers Euler classes, Chern classes, and Pontryagin classes. The second volume also received a favorable review by J. Eells in Mathematical Reviews.".
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- Foundations_of_Differential_Geometry wikiPageWikiLink Characteristic_class.
- Foundations_of_Differential_Geometry wikiPageWikiLink Chern_class.
- Foundations_of_Differential_Geometry wikiPageWikiLink Chern–Weil_homomorphism.
- Foundations_of_Differential_Geometry wikiPageWikiLink Chern–Weil_theory.
- Foundations_of_Differential_Geometry wikiPageWikiLink Complex_manifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Connection_(mathematics).
- Foundations_of_Differential_Geometry wikiPageWikiLink De_Rham_decomposition_theorem.
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- Foundations_of_Differential_Geometry wikiPageWikiLink Hopf-Rinow_theorem.
- Foundations_of_Differential_Geometry wikiPageWikiLink Hopf–Rinow_theorem.
- Foundations_of_Differential_Geometry wikiPageWikiLink Jacobi_field.
- Foundations_of_Differential_Geometry wikiPageWikiLink Kahlerian_manifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Katsumi_Nomizu.
- Foundations_of_Differential_Geometry wikiPageWikiLink Kähler_manifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Lie_group.
- Foundations_of_Differential_Geometry wikiPageWikiLink Manifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Mathematical_Reviews.
- Foundations_of_Differential_Geometry wikiPageWikiLink Morse_index.
- Foundations_of_Differential_Geometry wikiPageWikiLink Morse_theory.
- Foundations_of_Differential_Geometry wikiPageWikiLink Pontryagin_class.
- Foundations_of_Differential_Geometry wikiPageWikiLink Principal_bundle.
- Foundations_of_Differential_Geometry wikiPageWikiLink Rauch_comparison_theorem.
- Foundations_of_Differential_Geometry wikiPageWikiLink Riemannian_manifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Second_fundamental_form.
- Foundations_of_Differential_Geometry wikiPageWikiLink Shoshichi_Kobayashi.
- Foundations_of_Differential_Geometry wikiPageWikiLink Submanifold.
- Foundations_of_Differential_Geometry wikiPageWikiLink Symmetric_space.
- Foundations_of_Differential_Geometry wikiPageWikiLink Tensor.
- Foundations_of_Differential_Geometry wikiPageWikiLink Tensor_analysis.
- Foundations_of_Differential_Geometry wikiPageWikiLink Textbook.
- Foundations_of_Differential_Geometry wikiPageWikiLinkText "Foundations of Differential Geometry".
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- Foundations_of_Differential_Geometry subject Category:1963_books.
- Foundations_of_Differential_Geometry subject Category:1969_books.
- Foundations_of_Differential_Geometry subject Category:Mathematics_textbooks.
- Foundations_of_Differential_Geometry hypernym Book.
- Foundations_of_Differential_Geometry type Book.
- Foundations_of_Differential_Geometry type Work.
- Foundations_of_Differential_Geometry type Book.
- Foundations_of_Differential_Geometry type Work.
- Foundations_of_Differential_Geometry comment "Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.The first volume considers manifolds, fiber bundles, tensor analysis, connections in bundles, and the role of Lie groups.".
- Foundations_of_Differential_Geometry label "Foundations of Differential Geometry".
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