Homogeneous Structures on Riemannian Manifolds (London Mathematical Society Lecture Note Series, Series Number 83) (Volume 0) - Softcover

Tricerri, F.; Vanhecke, L.

Softcover

ISBN 10: 0521274893 ISBN 13: 9780521274890

Publisher: Cambridge University Press, 1983

Synopsis

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.

About this title

Book Description

The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1983
• Language: English
• ISBN 10: 0521274893
• ISBN 13: 9780521274890
• Binding: Paperback
• Edition number: 1
• Number of pages: 144