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AuthorJost, Jรผrgen. author
TitleRiemannian Geometry and Geometric Analysis [electronic resource] / by Jรผrgen Jost
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995
Connect tohttp://dx.doi.org/10.1007/978-3-662-03118-6
Descript XI, 404 p. online resource

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 Kรคhler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces


CONTENT

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 Kรคhler 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


Mathematics Mathematical analysis Analysis (Mathematics) System theory Differential geometry Calculus of variations Manifolds (Mathematics) Complex manifolds Physics Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Analysis Systems Theory Control Calculus of Variations and Optimal Control; Optimization Mathematical Methods in Physics



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