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.
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: June 1983
- format: Paperback
- isbn: 9780521274890
- length: 144 pages
- dimensions: 229 x 152 x 9 mm
- weight: 0.22kg
- availability: Available
Table of Contents
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.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×