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- Symmetric_space abstract "In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to formulate the inversion symmetry: via Riemannian geometry or via Lie theory. The Lie-theoretic definition is more general and more algebraic.In Riemannian geometry, the inversions are geodesic symmetries, and these are required to be isometries, leading to the notion of a Riemannian symmetric space. More generally, in Lie theory a symmetric space is a homogeneous space G/H for a Lie group G such that the stabilizer H of a point is an open subgroup of the fixed point set of an involution of G. This definition includes (globally) Riemannian symmetric spaces and pseudo-Riemannian symmetric spaces as special cases.Riemannian symmetric spaces arise in a wide variety of situations in both mathematics and physics. They were first studied extensively and classified by Élie Cartan. More generally, classifications of irreducible and semisimple symmetric spaces have been given by Marcel Berger. They are important in representation theory and harmonic analysis as well as differential geometry.".
- Symmetric_space wikiPageExternalLink item?id=ASENS_1957_3_74_2_85_0.
- Symmetric_space wikiPageID "1642877".
- Symmetric_space wikiPageRevisionID "599622308".
- Symmetric_space hasPhotoCollection Symmetric_space.
- Symmetric_space subject Category:Differential_geometry.
- Symmetric_space subject Category:Homogeneous_spaces.
- Symmetric_space subject Category:Lie_groups.
- Symmetric_space subject Category:Riemannian_geometry.
- Symmetric_space type Abstraction100002137.
- Symmetric_space type Attribute100024264.
- Symmetric_space type Group100031264.
- Symmetric_space type HomogeneousSpaces.
- Symmetric_space type LieGroups.
- Symmetric_space type Space100028651.
- Symmetric_space comment "In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to formulate the inversion symmetry: via Riemannian geometry or via Lie theory.".
- Symmetric_space label "Espace symétrique".
- Symmetric_space label "Symmetric space".
- Symmetric_space label "Symmetrischer Raum".
- Symmetric_space sameAs Symmetrischer_Raum.
- Symmetric_space sameAs Espace_symétrique.
- Symmetric_space sameAs m.05k14z.
- Symmetric_space sameAs Q3058244.
- Symmetric_space sameAs Q3058244.
- Symmetric_space sameAs Symmetric_space.
- Symmetric_space wasDerivedFrom Symmetric_space?oldid=599622308.
- Symmetric_space isPrimaryTopicOf Symmetric_space.