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Riemannian Geometry and Geometric Analysis

  • Textbook
  • © 1998

Overview

Authors:
  1. Jürgen Jost

    1. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

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  • Jost's book attempts a synthesis of geometric and analytic method on the way to Riemannian geometry and the author achieves this goal.
  • The result is an excellent book."
  • Acta Scientiarum Mathematicarum, 62.1996.
  • The new edition includes material on Ginzburg-Landau and Seiberg-Witten functionals, spin geometry, Dirac operators.

Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Foundational Material

    • Jürgen Jost
    Pages 1-77

  3. De Rham Cohomology and Harmonic Differential Forms

    • Jürgen Jost
    Pages 79-99

  4. Parallel Transport, Connections, and Covariant Derivatives

    • Jürgen Jost
    Pages 101-161

  5. Geodesics and Jacobi Fields

    • Jürgen Jost
    Pages 163-201

  6. A Short Survey on Curvature and Topology

    • Jürgen Jost
    Pages 203-209

  7. Morse Theory and Closed Geodesics

    • Jürgen Jost
    Pages 211-248

  8. Symmetric Spaces and Kähler Manifolds

    • Jürgen Jost
    Pages 249-299

  9. The Palais-Smale Condition and Closed Geodesics

    • Jürgen Jost
    Pages 301-314

  10. Harmonic Maps

    • Jürgen Jost
    Pages 315-422

  11. Variational Problems from Quantum Field Theory

    • Jürgen Jost
    Pages 423-437

  12. Back Matter

    Pages 439-458
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Keywords

About this book

From the reviews: "This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. It is a good introduction to Riemannian geometry. The book is made more interesting by the perspectives in various sections. where the author mentions the history and development of the material and provides the reader with references." Math. Reviews. The 2nd ed. includes new material on Ginzburg-Landau, Seibert-Witten functionals, spin geometry, Dirac operators.

Authors and Affiliations

  • Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Jürgen Jost

Bibliographic Information

  • Book Title: Riemannian Geometry and Geometric Analysis

  • Authors: Jürgen Jost

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-662-22385-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • eBook ISBN: 978-3-662-22385-7Published: 11 November 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: XIII, 458

  • Topics: Differential Geometry

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