Riemannian geometry and geometric analysis
By: Jürgen Jost.
Series: Universitext
Publisher: Springer
Published: 1995
Place of publication: Berlin; New York
Language: eng
Number of pages: 401
Subjects: Geometry, Riemannian.
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 Kähler manifolds; the Palais-Smale condition and closed geodesics; Harmonic maps, minimal surfaces.
Notes: Includes index.