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Riemannian Geometry and Geometric Analysis

Riemannian Geometry and Geometric Analysis
Catalogue Information
Field name Details
Dewey Class 516.36
Title Riemannian Geometry and Geometric Analysis ([EBook]) / by Jürgen Jost.
Author Jost, Jürgen. , 1956-
Other name(s) SpringerLink (Online service)
Publication Berlin, Heidelberg : Springer , 1995.
Physical Details XI, 404 pages : online resource.
Series Universitext 0172-5939
ISBN 9783662031186
Summary Note 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.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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