Riemannian Geometry and Geometric Analysis

✍ Scribed by Jürgen Jost (auth.)

• Publisher: Springer Berlin Heidelberg
• Year: 2002
• Tongue: English
• Leaves: 543
• Series: Universitext
• Category: Library

✦ Synopsis

The second edition featured a new chapter with a systematic development of variational problems from quantum field theory, in particular the Seiberg-Witten and Ginzburg-Landau functionals. This third edition gives a new presentation of Morse theory and Floer homology that emphasises the geometric aspects and integrates it into the context of Riemannian geometry and geometric analysis. It also gives a new presentation of the geometric aspects of harmonic maps: This uses geometric methods from the theory of geometric spaces of nonpositive curvature and, at the same time, sheds light on these, as an excellent example of the integration of deep geometric insights and powerful analytical tools. These new materials are based on a course at the University of Leipzig, entitled Geometry and Physics, attended by graduate students, postdocs and researchers from other areas of mathematics. Much of this material appears for the first time in a textbook.

✦ Table of Contents

Front Matter....Pages I-XIII
Foundational Material....Pages 1-78
De Rham Cohomology and Harmonic Differential Forms....Pages 79-99
Parallel Transport, Connections, and Covariant Derivatives....Pages 101-164
Geodesics and Jacobi Fields....Pages 165-230
Symmetric Spaces and Kähler Manifolds....Pages 231-279
Morse Theory and Floer Homology....Pages 281-372
Variational Problems from Quantum Field Theory....Pages 373-388
Harmonic Maps....Pages 389-514
Back Matter....Pages 515-535

✦ Subjects

Differential Geometry;Theoretical, Mathematical and Computational Physics