Homogeneous Structures on Riemannian Manifolds
1st Edition
Published on 28. May 2013
978-1-107-10768-7 (ISBN)
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. 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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
File size
4,45 MB
ISBN-13
978-1-107-10768-7 (9781107107687)
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Schweitzer Classification
Other editions
Additional editions
F. Tricerri | L. Vanhecke
Homogeneous Structures on Riemannian Manifolds
Book
06/1983
Cambridge University Press
€53.70
Shipment within 15-20 days
Content
1. The theorem of Ambrose and Singer; 2. Homogeneous Riemannian structures; 3. The eight classes of homogeneous structures; 4. Homogeneous structures on surfaces; 5. Homogeneous structures of type T1; 6. Naturally reductive homogeneous spaces and homogeneous structures of type T3; 7. The Heisenberg group; 8. Examples and the inclusion relations; 9. Generalized Heisenberg groups; 10.Self-dual and anti-self-dual homogeneous structures.
