Riemannian Geometry and Geometric Analysis

  • Jürgen Jost

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Jürgen Jost
    Pages 1-77
  3. Jürgen Jost
    Pages 163-201
  4. Jürgen Jost
    Pages 203-209
  5. Jürgen Jost
    Pages 211-248
  6. Jürgen Jost
    Pages 249-299
  7. Jürgen Jost
    Pages 315-422
  8. Back Matter
    Pages 439-458

About this book

Introduction

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 second edition contains a new chapter on variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. These topics are carefully and systematically developed, and the new edition contains a thorough treatment of the relevant background material, namely spin geometry and Dirac operators. The new material is based on a course "Geometry and Physics" at the University of Leipzig that was attented by graduate students, postdocs and researchers from other areas of mathematics. Much of the material is included here for the first time in a textbook, and the book will lead the reader to some of the hottest topics of contemporary mathematical research.

Keywords

Morse theory Riemannian geometry Seiber-Witten functionals curvature harmonic maps manifold symmetric spaces

Authors and affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-22385-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-63654-0
  • Online ISBN 978-3-662-22385-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
Industry Sectors
Aerospace
Oil, Gas & Geosciences