Definitions from Wikipedia (Symmetric space)

▸ noun:  A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point.
▸ noun:  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.


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