Riemannian geometry and geometric analysis
著者
書誌事項
Riemannian geometry and geometric analysis
（Universitext）
Springer, c2002
3rd ed
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
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 Kahler 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.
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