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... > topology > algebraic topology > manifold > differentiable manifold > Lie group > homogeneous space > symmetric space
... > geometry > topological space > manifold > differentiable manifold > Lie group > homogeneous space > symmetric space
... > geometry > differential geometry > differentiable manifold > Lie group > homogeneous space > symmetric space
... > topology > differential topology > differentiable manifold > Lie group > homogeneous space > symmetric space
... > algebra > group theory > topological group > Lie group > homogeneous space > symmetric space
algebra > abstract algebra > algebraic structure > homogeneous space > symmetric space
... > topology > algebraic topology > manifold > differentiable manifold > pseudo-Riemannian manifold > symmetric space
... > geometry > topological space > manifold > differentiable manifold > pseudo-Riemannian manifold > symmetric space
geometry > differential geometry > differentiable manifold > pseudo-Riemannian manifold > symmetric space
topology > differential topology > differentiable manifold > pseudo-Riemannian manifold > symmetric space

Preferred term

symmetric space  

Definition

  • In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of symmetries 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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Symmetric_space)

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http://data.loterre.fr/ark:/67375/PSR-SLL602JL-J

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RDF/XML TURTLE JSON-LD Created 8/31/23, last modified 8/31/23