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Riemannian Geometry and Geometric Analysis 1995. 2nd Printing ed. Edition
Author(s): Jurgen Jost (Author)
- Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date: 1 Jun. 1995
- Edition: 1995. 2nd Printing ed.
- Language: English
- Print length: 412 pages
- ISBN-10: 3540571132
- ISBN-13: 9783540571131
Book 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 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.
