{"product_id":"homogeneous-structures-on-riemannian-manifolds-paperback-9780521274890","title":"Homogeneous Structures on Riemannian Manifolds (Paperback) 9780521274890","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHomogeneous Structures on Riemannian Manifolds\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe central theme of this book is the theorem of Ambrose and Singer.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eF. Tricerri (Author), L. Vanhecke (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521274890, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 23 June 1983\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e144 pages\u003cbr\u003e22.8 x 15.2 x 0.8 cm, 0.22 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. The theorem of Ambrose and Singer\u003cbr\u003e 2. Homogeneous Riemannian structures\u003cbr\u003e 3. The eight classes of homogeneous structures\u003cbr\u003e 4. Homogeneous structures on surfaces\u003cbr\u003e 5. Homogeneous structures of type T1\u003cbr\u003e 6. Naturally reductive homogeneous spaces and homogeneous structures of type T3\u003cbr\u003e 7. The Heisenberg group\u003cbr\u003e 8. Examples and the inclusion relations\u003cbr\u003e 9. Generalized Heisenberg groups\u003cbr\u003e 10.Self-dual and anti-self-dual homogeneous structures.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006969893144,"sku":"9780521274890","price":46.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521274890i_ab0f6ac0-9834-448a-8ddd-83765cb5f0f9.jpg?v=1691374353","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/homogeneous-structures-on-riemannian-manifolds-paperback-9780521274890","provider":"Freshly Printed Books","version":"1.0","type":"link"}