Riemannian geometry and geometric analysis

Jürgen Jost3540773401, 9783540773405

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

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. [..] The book is made more interesting by the perspectives in various sections.” Mathematical Reviews

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Table of contents :
Cover……Page 1
Riemannian Geometry and Geometric Analysis, Fifth Edition……Page 3
ISBN 978-3-540-77340-5……Page 4
Preface……Page 6
Contents……Page 9
1 Foundational Material……Page 12
2 De Rham Cohomology and Harmonic Differential Forms……Page 97
3 Parallel Transport, Connections, and Covariant Derivatives……Page 123
4 Geodesics and Jacobi Fields……Page 188
5 Symmetric Spaces and Kähler Manifolds……Page 250
6 Morse Theory and Floer Homology……Page 307
7 Harmonic Maps between Riemannian Manifolds……Page 398
8 Harmonic maps from Riemann surfaces……Page 474
9 Variational Problems from Quantum Field Theory……Page 525
Appendix A Linear Elliptic Partial Differential Equations……Page 548
Appendix B Fundamental Groups and Covering Spaces……Page 559
Bibliography……Page 563
Index……Page 579