Homogeneous structures on Riemannian manifolds:
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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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1983
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| Schriftenreihe: | London Mathematical Society lecture note series
83 |
| Links: | https://doi.org/10.1017/CBO9781107325531 |
| 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. |
| Umfang: | 1 Online-Ressource (v, 125 Seiten) |
| ISBN: | 9781107325531 |
Internformat
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| 100 | 1 | |a Tricerri, F. |d 1947- | |
| 245 | 1 | 0 | |a Homogeneous structures on Riemannian manifolds |c F. Tricerri, L. Vanhecke |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1983 | |
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| 490 | 1 | |a London Mathematical Society lecture note series |v 83 | |
| 520 | |a 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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| spelling | Tricerri, F. 1947- Homogeneous structures on Riemannian manifolds F. Tricerri, L. Vanhecke Cambridge Cambridge University Press 1983 1 Online-Ressource (v, 125 Seiten) txt c cr London Mathematical Society lecture note series 83 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. Vanhecke, L. Erscheint auch als Druck-Ausgabe 9780521274890 |
| spellingShingle | Tricerri, F. 1947- Homogeneous structures on Riemannian manifolds |
| title | Homogeneous structures on Riemannian manifolds |
| title_auth | Homogeneous structures on Riemannian manifolds |
| title_exact_search | Homogeneous structures on Riemannian manifolds |
| title_full | Homogeneous structures on Riemannian manifolds F. Tricerri, L. Vanhecke |
| title_fullStr | Homogeneous structures on Riemannian manifolds F. Tricerri, L. Vanhecke |
| title_full_unstemmed | Homogeneous structures on Riemannian manifolds F. Tricerri, L. Vanhecke |
| title_short | Homogeneous structures on Riemannian manifolds |
| title_sort | homogeneous structures on riemannian manifolds |
| work_keys_str_mv | AT tricerrif homogeneousstructuresonriemannianmanifolds AT vanheckel homogeneousstructuresonriemannianmanifolds |