Einstein Manifolds [Paperback]

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. Einstein Manifold s is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.

Basic Material.- Basic Material (Continued): K?hler Manifolds.- Relativity.- Riemannian Functionals.- Ricci Curvature as a Partial Differential Equation.- Einstein Manifolds and Topology.- Homogeneous Riemannian Manifolds.- Compact Homogeneous K?hler Manifolds.- Riemannian Submersions.- Holonomy Groups.- K?hler-Einstein Metrics and the Calabi Conjecture.- The Moduli Space of Einstein Structures.- Self-Duality.- Quaternion-K?hler Manifolds.- A Report on the Non-Compact Case.- Generalizations of the Einstein Condition.

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 equeations, 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 onlc