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Homogeneous Structures on Riemannian Manifolds by F. Tricerri, G. Tricerri, L. Vanhecke

Homogeneous Structures on Riemannian Manifolds

by F. Tricerri , G. Tricerri , L. Vanhecke
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Book cover type: Paperback
  • ISBN13: 9780521274890
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 144
  • Original Price: USD 53.0
  • Language: English
  • Edition: N/A
  • Item Weight: 223 grams
  • BISAC Subject(s): Geometry / General

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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