Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Symmetric_space> ?p ?o }
- 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 wikiPageExternalLink Thesis%20Yong%20Dong%20Huang.pdf.
- Symmetric_space wikiPageID "1642877".
- Symmetric_space wikiPageLength "38774".
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- Symmetric_space wikiPageRevisionID "678358174".
- Symmetric_space wikiPageWikiLink Affine_connection.
- Symmetric_space wikiPageWikiLink Anti-de_Sitter_space.
- Symmetric_space wikiPageWikiLink Antilinear_map.
- Symmetric_space wikiPageWikiLink Atle_Selberg.
- Symmetric_space wikiPageWikiLink Automorphism.
- Symmetric_space wikiPageWikiLink Bott_periodicity_theorem.
- Symmetric_space wikiPageWikiLink Cartan_decomposition.
- Symmetric_space wikiPageWikiLink Cartan_subgroup.
- Symmetric_space wikiPageWikiLink Cartan–Ambrose–Hicks_theorem.
- Symmetric_space wikiPageWikiLink Category:Differential_geometry.
- Symmetric_space wikiPageWikiLink Category:Homogeneous_spaces.
- Symmetric_space wikiPageWikiLink Category:Lie_groups.
- Symmetric_space wikiPageWikiLink Category:Riemannian_geometry.
- Symmetric_space wikiPageWikiLink Cayley_plane.
- Symmetric_space wikiPageWikiLink Complete_metric_space.
- Symmetric_space wikiPageWikiLink Covariant_derivative.
- Symmetric_space wikiPageWikiLink Covering_space.
- Symmetric_space wikiPageWikiLink Curvature_of_a_connection.
- Symmetric_space wikiPageWikiLink De_Sitter_space.
- Symmetric_space wikiPageWikiLink Differentiable_manifold.
- Symmetric_space wikiPageWikiLink Differential_geometry.
- Symmetric_space wikiPageWikiLink Direct_sum_of_modules.
- Symmetric_space wikiPageWikiLink Double_Lagrangian_Grassmannian.
- Symmetric_space wikiPageWikiLink Ernest_Vinberg.
- Symmetric_space wikiPageWikiLink Euclidean_space.
- Symmetric_space wikiPageWikiLink Foundations_of_Differential_Geometry.
- Symmetric_space wikiPageWikiLink Freudenthal_magic_square.
- Symmetric_space wikiPageWikiLink Gelfand_pair.
- Symmetric_space wikiPageWikiLink General_relativity.
- Symmetric_space wikiPageWikiLink Geodesic.
- Symmetric_space wikiPageWikiLink Grassmannian.
- Symmetric_space wikiPageWikiLink Group_action.
- Symmetric_space wikiPageWikiLink Harmonic_analysis.
- Symmetric_space wikiPageWikiLink Hermitian_symmetric_space.
- Symmetric_space wikiPageWikiLink Holonomy.
- Symmetric_space wikiPageWikiLink Homogeneous_space.
- Symmetric_space wikiPageWikiLink Homotopy_group.
- Symmetric_space wikiPageWikiLink Hyperbolic_space.
- Symmetric_space wikiPageWikiLink If_and_only_if.
- Symmetric_space wikiPageWikiLink Indecomposable_module.
- Symmetric_space wikiPageWikiLink Involution_(mathematics).
- Symmetric_space wikiPageWikiLink Irreducible_representation.
- Symmetric_space wikiPageWikiLink Isometry_(Riemannian_geometry).
- Symmetric_space wikiPageWikiLink Jet_bundle.
- Symmetric_space wikiPageWikiLink Katsumi_Nomizu.
- Symmetric_space wikiPageWikiLink Klein_geometry.
- Symmetric_space wikiPageWikiLink Lagrangian_Grassmannian.
- Symmetric_space wikiPageWikiLink Lie_group.
- Symmetric_space wikiPageWikiLink Lie_theory.
- Symmetric_space wikiPageWikiLink Loop_space.
- Symmetric_space wikiPageWikiLink Marcel_Berger.
- Symmetric_space wikiPageWikiLink Minkowski_space.
- Symmetric_space wikiPageWikiLink Octonion.
- Symmetric_space wikiPageWikiLink Orthogonal_group.
- Symmetric_space wikiPageWikiLink Orthogonal_symmetric_Lie_algebra.
- Symmetric_space wikiPageWikiLink Parallel_transport.
- Symmetric_space wikiPageWikiLink Projective_space.
- Symmetric_space wikiPageWikiLink Pseudo-Riemannian_manifold.
- Symmetric_space wikiPageWikiLink Quaternion.
- Symmetric_space wikiPageWikiLink Quaternion-Kähler_symmetric_space.
- Symmetric_space wikiPageWikiLink Quaternionic_vector_space.
- Symmetric_space wikiPageWikiLink Representation_theory.
- Symmetric_space wikiPageWikiLink Restricted_root_system.
- Symmetric_space wikiPageWikiLink Riemannian_geometry.
- Symmetric_space wikiPageWikiLink Satake_diagram.
- Symmetric_space wikiPageWikiLink Sectional_curvature.
- Symmetric_space wikiPageWikiLink Semisimple_Lie_algebra.
- Symmetric_space wikiPageWikiLink Simple_Lie_group.
- Symmetric_space wikiPageWikiLink Simply_connected_space.
- Symmetric_space wikiPageWikiLink Sphere.
- Symmetric_space wikiPageWikiLink Tangent_space.
- Symmetric_space wikiPageWikiLink Torsion-free.
- Symmetric_space wikiPageWikiLink Unitary_representation.
- Symmetric_space wikiPageWikiLink Versor.
- Symmetric_space wikiPageWikiLink Élie_Cartan.
- Symmetric_space wikiPageWikiLinkText "Riemannian symmetric space".
- Symmetric_space wikiPageWikiLinkText "Riemannian symmetric spaces".
- Symmetric_space wikiPageWikiLinkText "Symmetric space".
- Symmetric_space wikiPageWikiLinkText "Symmetric_space#Weakly_symmetric_Riemannian_spaces".
- Symmetric_space wikiPageWikiLinkText "another meaning".
- Symmetric_space wikiPageWikiLinkText "intrinsic geometry".
- Symmetric_space wikiPageWikiLinkText "locally symmetric".
- Symmetric_space wikiPageWikiLinkText "symmetric decomposition".
- Symmetric_space wikiPageWikiLinkText "symmetric space of compact type".
- Symmetric_space wikiPageWikiLinkText "symmetric space".
- Symmetric_space wikiPageWikiLinkText "symmetric".
- Symmetric_space wikiPageUsesTemplate Template:Citation.
- Symmetric_space wikiPageUsesTemplate Template:Cite_journal.
- Symmetric_space wikiPageUsesTemplate Template:Harv.
- Symmetric_space wikiPageUsesTemplate Template:Harvtxt.
- Symmetric_space wikiPageUsesTemplate Template:Lie_groups.
- Symmetric_space wikiPageUsesTemplate Template:Main.
- Symmetric_space wikiPageUsesTemplate Template:Other_uses.