Riemannian geometry and geometric analysis
著者
書誌事項
Riemannian geometry and geometric analysis
（Universitext）
Springer, c2008
5th ed
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注記
Includes bibliographical references (p. [561]-576) and index
内容説明・目次
内容説明
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. This new edition introduces and explains the ideas of the parabolic methods that have recently found such spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.
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.- Harmonic Maps between Riemannian Manifolds.- Harmonic Maps from Riemann Surfaces.- Variational Problems from Quantum Field Theory.- Appendix A: Linear Elliptic Partial Differential Equations.- Appendix B: Fundamental Groups and Covering Spaces.- Bibliography.- Index.
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