Riemannian Geometry and Geometric Analysis

by Jürgen Jost

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

Genres: Mathematics, Geometry, Science

401 pages, Paperback

First published September 18, 1997

About the author

Jürgen Jost is a German mathematician. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.