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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Homogeneous Structures on Riemannian Manifolds

Homogeneous Structures on Riemannian Manifolds

Tricerri, F.
Vanhecke, L.
Tricerri, G.

Paperback

Series: London Mathematical Society Lecture Note, Book 83

General MathematicsGeometry

ISBN10: 0521274893
ISBN13: 9780521274890
Publisher: Cambridge University Press
Published: Jun 23 1983
Pages: 144
Weight: 0.49
Height: 0.34 Width: 6.00 Depth: 9.00
Language: English
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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