Apress NBA

Riemannian Geometry and Geometric Analysis

By Jürgen Jost

  • eBook Price: $59.95
Buy eBook Buy Print Book

Riemannian Geometry and Geometric Analysis Cover Image

This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.

Full Description

  • Add to Wishlist
  • ISBN13: 978-3-6422-1297-0
  • 624 Pages
  • Publication Date: July 28, 2011
  • Available eBook Formats: PDF
Full Description
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
Table of Contents

Table of Contents

  1. 1. Riemannian Manifolds.
  2. 2. Lie Groups and Vector Bundles.
  3. 3. The Laplace Operator and Harmonic Differential Forms.
  4. 4. Connections and Curvature.
  5. 5. Geodesics and Jacobi Fields.
  6. 6. Symmetric Spaces and K¨ahler Manifolds.
  7. 7. Morse Theory and Floer Homology.
  8. 8. Harmonic Maps between Riemannian Manifolds.
  9. 9. Harmonic Maps from Riemann Surfaces.
  10. 10. Variational Problems from Quantum Field Theory.
  11. A. Linear Elliptic Partial Differential Equations.
  12. A.1 Sobolev Spaces.
  13. A.2 Linear Elliptic Equations.
  14. A.3 Linear Parabolic Equations.
  15. B. Fundamental Groups and Covering Spaces.
  16. Bibliography.
  17. Index.

If you think that you've found an error in this book, please let us know by emailing to editorial@apress.com . You will find any confirmed erratum below, so you can check if your concern has already been addressed.
No errata are currently published


    1. PHP Objects, Patterns, and Practice


      View Book

    2. Beginning Android 3D Game Development


      View Book

    3. Troubleshooting Oracle Performance


      View Book

    4. Beginning Amazon Web Services with Node.js


      View Book