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  • © 2011

Riemannian Geometry and Geometric Analysis

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  • Continues to lead its readers to some of the hottest topics of contemporary mathematical research

  • Each chapter ends with a set of exercises

  • The 6th edition includes a systematic treatment of eigenvalues of Riemannian manifolds and several other addition

Part of the book series: Universitext (UTX)

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  • ISBN: 978-3-642-21298-7
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
  2. Chapter 1 Riemannian Manifolds

    • Jürgen Jost
    Pages 1-39
  3. Chapter 2 Lie Groups and Vector Bundles

    • Jürgen Jost
    Pages 41-87
  4. Chapter 4 Connections and Curvature

    • Jürgen Jost
    Pages 133-204
  5. Chapter 5 Geodesics and Jacobi Fields

    • Jürgen Jost
    Pages 205-259
  6. A Short Survey on Curvature and Topology

    • Jürgen Jost
    Pages 261-268
  7. Chapter 7 Morse Theory and Floer Homology

    • Jürgen Jost
    Pages 327-417
  8. Back Matter

    Pages 571-611

About this book

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  

Keywords

  • 53B21, 53L20, 32C17, 35I60, 49-XX, 58E20, 57R15
  • Dirac operator
  • Morse theory
  • Riemannian geometry
  • curvature
  • geodesic
  • harmonic map

Authors and Affiliations

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

    Jürgen Jost

About the author

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.

Bibliographic Information

Buying options

eBook
USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-21298-7
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout