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＜電子ブック＞
Riemannian Geometry and Geometric Analysis / by Jürgen Jost
(Universitext. ISSN:21916675)

版	1st ed. 1995.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1995
本文言語	英語
大きさ	XI, 404 p : online resource
著者標目	*Jost, Jürgen author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Manifolds (Mathematics) LCSH:Mathematical analysis LCSH:System theory LCSH:Control theory LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Mathematical physics FREE:Differential Geometry FREE:Manifolds and Cell Complexes FREE:Analysis FREE:Systems Theory, Control FREE:Calculus of Variations and Optimization FREE:Mathematical Methods in Physics
一般注記	1. Foundational Material -- 2. De Rham Cohomology and Harmonic Differential Forms -- 3. Parallel Transport, Connections, and Covariant Derivatives -- 4. Geodesics and Jacobi Fields -- A Short Survey on Curvature and Topology -- 5. Morse Theory and Closed Geodesics -- 6. Symmetric Spaces and Kähler Manifolds -- 7. The Palais-Smale Condition and Closed Geodesics -- 8. Harmonic Maps -- Appendix A: Linear Elliptic Partial Differential Equations -- A.1 Sobolev Spaces -- A.2 Existence and Regularity Theory for Solutions of Linear Elliptic Equations -- Appendix B: Fundamental Groups and Covering Spaces This textbook introduces techniques from nonlinear analysis at an early stage. Such techniques have recently become an indispensable tool in research in geometry, and they are treated here for the first time in a textbook. Topics treated include: Differentiable and Riemannian manifolds, metric properties, tensor calculus, vector bundles; the Hodge Theorem for de Rham cohomology; connections and curvature, the Yang-Mills functional; geodesics and Jacobi fields, Rauch comparison theorem and applications; Morse theory (including an introduction to algebraic topology), applications to the existence of closed geodesics; symmetric spaces and Kähler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces HTTP:URL=https://doi.org/10.1007/978-3-662-03118-6

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