Symmetric Space

In differential geometry, portrayal hypothesis and symphonious investigation, a symmetric space is a pseudo-Riemannian complex whose gathering of balances contains a reversal evenness about each point.In geometric terms, a total, just associated Riemannian complex is a symmetric space if and just if its ebb and flow tensor is invariant under equal vehicle. All the more for the most part, a Riemannian complex (M, g) is supposed to be symmetric if and just if, for each point p of M, there exists an isometry of M fixing p and following up on the digression space {\displaystyle T_{p}M}T_{p}M as less the personality. The two depictions can likewise normally be stretched out to the setting of pseudo-Riemannian manifolds.

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