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Homogeneous Structures on Riemannian Manifolds

By: F. Tricerri, G. Tricerri, L. Vanhecke

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Paperback | 22 August 1983

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144 Pages

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22.86 x 15.24 x 0.86

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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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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Applied Mathematics Topology

The theorem of Ambrose and Singer
Homogeneous Riemannian structures
The eight classes of homogeneous structures
Homogeneous structures on surfaces
Homogeneous structures of type T1
Naturally reductive homogeneous spaces and homogeneous structures of type T3
The Heisenberg group
Examples and the inclusion relations
Generalized Heisenberg groups
Self-dual and anti-self-dual homogeneous structures
Table of Contents provided by Publisher. All Rights Reserved.

Homogeneous Structures on Riemannian Manifolds

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Paperback

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