Riemannian Geometry and Geometric Analysis (eBook, 2002) [WorldCat.org]
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Riemannian Geometry and Geometric Analysis

Author: Jürgen Jost
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2002.
Series: Universitext.
Edition/Format:   eBook : Document : English : Third editionView all editions and formats
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jürgen Jost
ISBN: 9783662046722 3662046725
OCLC Number: 851382709
Description: 1 online resource (xiii, 535 pages)
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.
Series Title: Universitext.
Responsibility: by Jürgen Jost.

Abstract:

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.

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