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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