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Riemannian Geometry and Geometric Analysis

  • Jürgen Jost

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Jürgen Jost
    Pages 1-54
  3. Jürgen Jost
    Pages 125-163
  4. Jürgen Jost
    Pages 165-171
  5. Jürgen Jost
    Pages 173-210
  6. Jürgen Jost
    Pages 211-261
  7. Jürgen Jost
    Pages 277-384
  8. Back Matter
    Pages 385-404

About this book

Introduction

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.

Keywords

Harmonische Abbildungen Hodge theorem Levi-Civita connection Lovi-Civita-Zusammenhang Minimalflächen Morse theory Morse-Theorie Rauch comparison theorem Rauchscher Vergleichssatz Riemannian m curvature geodesics harmonic maps minimal surfaces

Authors and affiliations

  • Jürgen Jost
    • 1
  1. 1.Institut für MathematikUniversität BochumBochumGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03118-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57113-1
  • Online ISBN 978-3-662-03118-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site