Riemannian Geometry and Geometric Analysis /
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 prope...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
1995.
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| Series: | Universitext,
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xi, 404 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| ISBN: | 9783662031186 (electronic bk.) 3662031183 (electronic bk.) |
| ISSN: | 0172-5939 |