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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.

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rdfs:label	Foundations of Differential Geometry (en) Foundations of Differential Geometry (pt)
rdfs: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. (en) Foundations of Differential Geometry é uma obra enciclopédica em dois volumes elaborada pelos matemáticos japoneses Shoshichi Kobayashi e Katsumi Nomizu, a qual trata sobre geometria diferencial. O primeiro volume foi publicado originalmente em 1963 e o segundo, em 1969, pela Interscience Publishers. Uma versão atualizada foi lançada nos Estados Unidos em 1996 pela Wiley Classics Library. (pt)
dcterms:subject	1963 non-fiction books 1969 non-fiction books Mathematics textbooks
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Link from a Wikipage to another Wikipage	Morse index Homogeneous space Hopf–Rinow theorem Characteristic class Jacobi field Lie group Connection (mathematics) Mathematical analysis Gauss map Geodesic Geometry Submanifold Shoshichi Kobayashi Complex manifold Symmetric space Mathematical Reviews Pontryagin class Fiber bundle Riemann curvature tensor Riemannian manifold 1963 non-fiction books James Eells Textbook 1969 non-fiction books Mathematics textbooks Abstract algebra Chern class Katsumi Nomizu Holonomy Differential geometry Manifold Bulletin of the AMS Tensor analysis Kähler manifold Cartan–Hadamard theorem Second fundamental form Euler class Principal bundle Exercise (mathematics) Chern–Weil theory Rauch comparison theorem De Rham decomposition theorem
Link from a Wikipage to an external page	https://www.ams.org/journals/bull/1964-70-02/S0002-9904-1964-11094-6/%7Cdoi=10.1090/s0002-9904-1964-11094-6%7Cdoi-access=free https://www.ams.org/mathscinet/pdf/0152974.pdf https://www.ams.org/mathscinet/pdf/0238225.pdf
sameAs	Foundations of Differential Geometry Foundations of Differential Geometry Foundations of Differential Geometry Foundations of Differential Geometry Foundations of Differential Geometry
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has 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 James 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, Jacobi fields, the Morse index, the Rauch comparison theorems, and the Cartan–Hadamard theorem. Then it ascends to complex manifolds, Kähler 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. (en) Foundations of Differential Geometry é uma obra enciclopédica em dois volumes elaborada pelos matemáticos japoneses Shoshichi Kobayashi e Katsumi Nomizu, a qual trata sobre geometria diferencial. O primeiro volume foi publicado originalmente em 1963 e o segundo, em 1969, pela Interscience Publishers. Uma versão atualizada foi lançada nos Estados Unidos em 1996 pela Wiley Classics Library. O primeiro volume do livro focaliza principalmente o âmbito da geometria que trata sobre variedade, maço de fibras, tensor, conexão, grupo de Lie, teorema de decomposição de De Rham e o . O segundo, por outro lado, é mais específico em seus assuntos: variedade de Riemann, e a . (pt)
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is Link from a Wikipage to another Wikipage of	Vector-valued differential form Homogeneous space Ricci curvature Curvature form Curvature of Riemannian manifolds Canonical connection List of important publications in mathematics Normal coordinates Ehresmann connection Connection (principal bundle) Connection (vector bundle) Shoshichi Kobayashi Adjoint bundle Linear complex structure List of Brown University faculty Ring of polynomial functions

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