Riemannian Geometry and Geometric Analysis
532 pages, parution le 21/01/2002
(3eme édition)
Résumé
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.
Appendix B: Fundamental Groups and Covering Spaces
Index
Contents
- Foundational 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 B: Fundamental Groups and Covering Spaces
Index
L'auteur - Jürgen Jost
Honorary Professor, Department of Mathematics,
University of Leipzig
Member, Academy of Sciences and Literature, Mainz, the
Saxonian Academy of Sciences, Leipzig, and the German
Academy of the Natural Scientists - Leopoldina
External Faculty Member, Santa Fe Institute for the
Sciences of Complexity, 1399 Hyde Park Road, Santa Fe, NM
87501, USA
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Jürgen Jost |
| Parution | 21/01/2002 |
| Édition | 3eme édition |
| Nb. de pages | 532 |
| Format | 15,5 x 23,5 |
| Couverture | Broché |
| Poids | 837g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540426271 |
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