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{"type":"standard","title":"Symmetric space","displaytitle":"Symmetric space","namespace":{"id":0,"text":""},"wikibase_item":"Q3058244","titles":{"canonical":"Symmetric_space","normalized":"Symmetric space","display":"Symmetric space"},"pageid":1642877,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/330px-E8Petrie.svg.png","width":320,"height":321},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/2852px-E8Petrie.svg.png","width":2852,"height":2863},"lang":"en","dir":"ltr","revision":"1255379034","tid":"637fc3e8-9acf-11ef-9ae5-6890534feb4a","timestamp":"2024-11-04T17:08:19Z","description":"(pseudo-)Riemannian manifold whose geodesics are reversible","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Symmetric_space","revisions":"https://en.wikipedia.org/wiki/Symmetric_space?action=history","edit":"https://en.wikipedia.org/wiki/Symmetric_space?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Symmetric_space"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Symmetric_space","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Symmetric_space","edit":"https://en.m.wikipedia.org/wiki/Symmetric_space?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Symmetric_space"}},"extract":"In mathematics, a symmetric space is a Riemannian manifold whose group of isometries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis.","extract_html":"
In mathematics, a symmetric space is a Riemannian manifold whose group of isometries contains an inversion symmetry about every point. This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in differential geometry, representation theory and harmonic analysis.
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