Riemannian Geometry and Geometric Analysis

• Main Author: Jost, Jürgen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Universitext,
• Subjects: Mathematics.; Differential geometry.; Physics.; Differential Geometry.; Theoretical, Mathematical and Computational Physics.

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...

Table of Contents:

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