Science Fair Project Encyclopedia
Riemannian symmetric space
In mathematics, including applications to general relativity, a (Riemannian) symmetric space in differential geometry is a certain kind of homogeneous space in the theory of Lie groups.
A geometric characterization is that it is a Riemannian manifold such that for every point there exists an isometry fixing that point and inducing minus the identity on the tangent space at that point. A Lie group characterisation is as G/H where G is a Lie group and H a subgroup that is open in the fixed set of an automorphism of G of order 2. There is a classification of such spaces, by Elie Cartan.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details