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...

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Bibliographische Detailangaben

1. Verfasser:	Tricerri, F. 1947- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 1983
Schriftenreihe:	London Mathematical Society lecture note series 83
Schlagworte:	Riemannian manifolds Riemannscher Raum
Online-Zugang:	BSB01 FHN01 Volltext
Zusammenfassung:	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
Beschreibung:	Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Beschreibung:	1 online resource (v, 125 pages)
ISBN:	9781107325531
DOI:	10.1017/CBO9781107325531