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Einstein Manifolds / by Arthur L. Besse
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Classics in Mathematics | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2008Description: Online-Ressource (X, 516 p, digital)ISBN:- 9783540743118
- 516.362
- 514.34
- QA613-613.8 QA613.6-613.66
- QA649
Contents:
Summary: Basic Material -- Basic Material (Continued): Kähler Manifolds -- Relativity -- Riemannian Functionals -- Ricci Curvature as a Partial Differential Equation -- Einstein Manifolds and Topology -- Homogeneous Riemannian Manifolds -- Compact Homogeneous Kähler Manifolds -- Riemannian Submersions -- Holonomy Groups -- Kähler-Einstein Metrics and the Calabi Conjecture -- The Moduli Space of Einstein Structures -- Self-Duality -- Quaternion-Kähler Manifolds -- A Report on the Non-Compact Case -- Generalizations of the Einstein Condition.Summary: From the reviews: "[...] an efficient reference book for many fundamental techniques of Riemannian geometry. [...] despite its length, the reader will have no difficulty in getting the feel of its contents and discovering excellent examples of all interaction of geometry with partial differential equations, topology, and Lie groups. Above all, the book provides a clear insight into the scope and diversity of problems posed by its title." S.M. Salamon in MathSciNet 1988 "It seemed likely to anyone who read the previous book by the same author, namely "Manifolds all of whose geodesic are closed", that the present book would be one of the most important ever published on Riemannian geometry. This prophecy is indeed fulfilled." T.J. Wilmore in Bulletin of the London Mathematical Society 1987.PPN: PPN: 1649948883Package identifier: Produktsigel: ZDB-2-SMA | ZDB-2-BAE | ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
CONTENTS; Chapter 0. Introduction; Chapter 1. Basic Material; Chapter 2. Basic Material (Continued): Kahler Manifolds; Chapter 3. Relativity; Chapter 4. Riemannian Functionals; Chapter 5. Ricci Curvature as a Partial Differential Equation; Chapter 6. Einstein Manifolds and Topology; Chapter 7. Homogeneous Riemannian Manifolds; Chapter 8. Compact Homogeneous Kahler Manifolds; Chapter 9. Riemannian Submersions; Chapter 10. Holonomy Groups; Chapter 11. Kahler-Einstein Metrics and the Calabi Conjecture; Chapter 12. The Moduli Space of Einstein Structures; Chapter 13. Self-Duality
Chapter 14. Quaternion-Kahler ManifoldsChapter 15. A Report on the Non-Compact Case; Chapter 16. Generalizations of the Einstein Condition; Appendix. Sobolev Spaces and Elliptic Operators; Addendum; Bibliography; Notation Index; Subject Index; Errata
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