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Homogeneous Structures on Riemannian Manifolds (Electronic book text)
Homogeneous Structures on Riemannian Manifolds (Electronic book text): Franco Tricerri, L. Vanhecke
Homogeneous Structures on Riemannian Manifolds (Electronic book text): Franco Tricerri, L. Vanhecke

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Homogeneous Structures on Riemannian Manifolds (Electronic book text)

Franco Tricerri, L. Vanhecke

Series: London Mathematical Society Lecture Note Series, 83

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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.

General

Imprint: Cambridge UniversityPress
Country of origin: United Kingdom
Series: London Mathematical Society Lecture Note Series, 83
Release date: May 2013
Authors: Franco Tricerri • L. Vanhecke
Format: Electronic book text
Pages: 144
ISBN-13: 978-1-107-10768-7
Barcode: 9781107107687
Categories: Promotions
Books > Science & Mathematics > Mathematics > Geometry
Books > Science & Mathematics > Mathematics > Geometry > General
LSN: 1-107-10768-7

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