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  1. Home
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  3. Homogeneous Structures on Riemannian Manifolds
  • Cited by 120
Publisher:
Cambridge University Press
Online publication date:
April 2013
Print publication year:
1983
Online ISBN:
9781107325531
DOI:
https://doi.org/10.1017/CBO9781107325531
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
London Mathematical Society Lecture Note Series (83)
Information

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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