リーマン幾何学および幾何解析（第３版） Riemannian Geometry and Geometric Analysis (Universitext) （XIII, 532 p. 23,5 cm）

Jost, Juergen

SPRINGER, BERLIN

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 532 p.
• 商品コード 9783540426271

基本説明

３年振りの改訂版。
Contents: Fundamental Material; De Rham Cohomology and Harmonic Differential Forms; Parallel Transport, Connections, and Covariant Derivatives; and more.

Description

(Text)
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 content)
From the contents:
- Fundamental Material
- De Rham Cohomology and Harmonic Differential Forms
- Parallel Transport, Connections, and Covariant Derivatives
- Geodesics and Jacobi Fields
- A Short Survey on Curvature and Topology: Symmetric Spaces and Kähler Manifolds
- Morse theory and Floer homology
- Variational Problems from Quantum Field Theory
- Harmonic Maps
- Appendix A: Linear Elliptic Partial Differential Equations
- Appendix B: Fundamental Groups and Covering Spaces
- Index