๐”– Scriptorium
โœฆ   LIBER   โœฆ
๐Ÿ“

Riemannian Geometry and Geometric Analysis

โœ Scribed by Jรผrgen Jost (auth.)

Publisher
Springer-Verlag Berlin Heidelberg
Year
2011
Tongue
English
Leaves
626
Series
Universitext
Edition
6
Category
Library
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โœฆ Synopsis

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 โ€˜Perspectivesโ€™, written with the aim to place the material in a broader context and explain further results and directions." Zentralblatt MATH

โœฆ Table of Contents

Front Matter....Pages i-xiii
Chapter 1 Riemannian Manifolds....Pages 1-39
Chapter 2 Lie Groups and Vector Bundles....Pages 41-87
Chapter 3 The Laplace Operator and Harmonic Differential Forms....Pages 89-131
Chapter 4 Connections and Curvature....Pages 133-204
Chapter 5 Geodesics and Jacobi Fields....Pages 205-259
A Short Survey on Curvature and Topology....Pages 261-268
Chapter 6 Symmetric Spaces and Kรคhler Manifolds....Pages 269-325
Chapter 7 Morse Theory and Floer Homology....Pages 327-417
Chapter 8 Harmonic Maps between Riemannian Manifolds....Pages 419-494
Chapter 9 Harmonic Maps from Riemann Surfaces....Pages 495-545
Chapter 10 Variational Problems from Quantum Field Theory....Pages 547-569
Back Matter....Pages 571-611

โœฆ Subjects

Differential Geometry;Theoretical, Mathematical and Computational Physics

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