Homogeneous Structures on Riemannian Manifolds
Book Details
Format
Paperback / Softback
Book Series
London Mathematical Society Lecture Note Series
ISBN-10
0521274893
ISBN-13
9780521274890
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 23rd, 1983
Print length
144 Pages
Weight
220 grams
Dimensions
22.80 x 15.20 x 0.80 cms
Product Classification:
Geometry
Ksh 9,550.00
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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.
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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