ENGLISH

Riemannian Geometry and Geometric Analysis

By Jürgen Jost (auth.)

Book information

Publisher
Springer Berlin Heidelberg
Year
1995
ISBN
978-3-540-57113-1, 978-3-662-03118-6
DOI
10.1007/978-3-662-03118-6
Language
english
Format
PDF
Filesize
7 MB (7386242 bytes)
Series
Universitext
Pages
XI, 404 p.\406
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Control;Calculus of Variations and Optimal ControlDifferential Geometry;Manifolds and Cell Complexes

Description

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 K?hler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces.

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