Symmetric space
id:
symmetric-space-215-2007874
title:
Symmetric space
text:
In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-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. In geomet
brand slug:
wiki
category slug:
encyclopedia
description:
A (pseudo-)Riemannian manifold whose geodesics are reversible.
original url:
https://en.wikipedia.org/wiki/Symmetric_space
date created:
2005-03-24T09:58:36Z
date modified:
2024-09-12T19:50:15Z
main entity:
{"identifier":"Q3058244","url":"https://www.wikidata.org/entity/Q3058244"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/1/14/E8Petrie.svg","width":512,"height":514}
fields total:
13
integrity:
16