Universitext

Riemannian Geometry and Geometric Analysis

Authors: Jost, Jürgen

  • Established textbook
  • Continues to lead its readers to some of the hottest topics of contemporary mathematical research
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  • ISBN 978-3-642-21298-7
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About this Textbook

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discussed further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.

The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other additions. Also, the entire material has been reorganized in order to improve the coherence of the book.

From the reviews:
"This book provides a very readable introduction to Riemannian geometry and geometric analysis. ... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome." Mathematical Reviews

"...the material ... is self-contained. Each chapter ends with a set of exercises. Most of the paragraphs have a section ‘Perspectives’, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH  

About the authors

Jürgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA.

He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007), Differentialgeometrie und MInimalflächen (1994, 2007, with J. Eschenburg), Dynamical Systems (2005), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals.

Table of contents (11 chapters)

  • Chapter 1 Riemannian Manifolds

    Jost, Jürgen

    Pages 1-39

  • Chapter 2 Lie Groups and Vector Bundles

    Jost, Jürgen

    Pages 41-87

  • Chapter 3 The Laplace Operator and Harmonic Differential Forms

    Jost, Jürgen

    Pages 89-131

  • Chapter 4 Connections and Curvature

    Jost, Jürgen

    Pages 133-204

  • Chapter 5 Geodesics and Jacobi Fields

    Jost, Jürgen

    Pages 205-259

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-3-642-21298-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.95
price for USA
  • ISBN 978-3-642-21297-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Riemannian Geometry and Geometric Analysis
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21298-7
DOI
10.1007/978-3-642-21298-7
Softcover ISBN
978-3-642-21297-0
Series ISSN
0172-5939
Edition Number
6
Number of Pages
XIII, 611
Number of Illustrations and Tables
12 b/w illustrations, 4 illustrations in colour
Topics