Description
Book SynopsisEinstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.
Trade ReviewFrom 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 on Riemannian geometry. This prophecy is indeed fulfilled."
T.J. Wilmore in Bulletin of the London Mathematical Society 1987
"Einstein Manifolds is accordingly described as Besse’s second book … . there is no doubt that Einstein Manifolds is a magnificient work of mathematical scholarship. … It is truly a seminal work on an incomparably fascinating and important subject." (Michael Berg, MathDL, March, 2008)
"The present book is intended to be a complete reference book. … The book under review serves several purposes. It is an efficient reference for many fundamental techniques of Riemannian geometry as well as excellent examples of the interaction of geometry with partial differential equations, topology and Lie groups. Certainly the monograph provides a clear insight into the scope and diversity of problems posed by its title." (Adela-Gabriela Mihai, Zentralblatt MATH, Vol. 1147, 2008)
Table of ContentsBasic 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.
