Homogeneous Structure on Riemannian Manifolds by Franco Tricerri
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Homogeneous Structure on Riemannian Manifolds
By Franco Tricerri

Homogeneous Structure on Riemannian Manifolds

By (author) See other recent books by Franco Tricerri See other recent books by L. Vanhecke
Format: Paperback

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Homogeneous Structure on Riemannian Manifolds by Franco Tricerri

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. 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.

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Book Details

ISBN: 9780521274890
ISBN-10: 0521274893
Format: Paperback
(228mm x 152mm x 9mm)
Pages: 144
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 23-Jun-1983
Country of Publication: United Kingdom

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