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  3. Homogeneous Structures on Riemannian Manifolds
  • Cited by 130
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    • Publisher:
      Cambridge University Press
      Publication date:
      April 2013
      June 1983
      ISBN:
      9781107325531
      9780521274890
      DOI:
      https://doi.org/10.1017/CBO9781107325531
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.22kg, 144 Pages
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology
      Series:
      London Mathematical Society Lecture Note Series (83)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (83)
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    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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