About: Hermitian symmetric space

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In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds.

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rdf:type	Thing yago:WikicatLieGroups yago:Abstraction100002137 yago:Attribute100024264 yago:Group100031264 yago:WikicatHomogeneousSpaces yago:Space100028651
rdfs:label	Hermitescher symmetrischer Raum (de) Hermitian symmetric space (en)
rdfs:comment	In der Mathematik ist ein hermitescher symmetrischer Raum eine hermitesche Mannigfaltigkeit, die gleichzeitig ein symmetrischer Raum ist. Beispiele sind die riemannsche Zahlenkugel, die hyperbolische Ebene oder der siegelsche Halbraum. Hermitesche symmetrische Räume werden in der algebraischen Geometrie als Parameterräume für die verwendet. (de) In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. (en)
rdfs:seeAlso	Mutation (Jordan algebra)
dcterms:subject	Complex manifolds Differential geometry Homogeneous spaces Lie groups Riemannian geometry
Wikipage page ID	4127357 (xsd:integer)
Wikipage revision ID	1113209873 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Ludwig Siegel Euclidean Hurwitz algebra Euler–Poincaré characteristic Totally geodesic Bergman kernel Complex manifolds Invariant convex cone Lie group Jordan frame (Jordan algebra) Shilov boundary Differential geometry Compact space Complexification (Lie group) Convex set Mathematics Nilradical of a Lie algebra Operator norm Grassmannian Mutation (Jordan algebra) Möbius transformation Real manifold Bergman metric Lexicographic order Lie algebra Homogeneous spaces Complete metric space Complex geometry Complex manifold Complex projective space Composition algebra Élie Cartan Fubini–Study metric Identity component Symmetric space Cayley transform Adjoint representation Algebraic groups Lie groups Graded Lie algebra Projective variety Riemannian metric Riemannian symmetric space Harish-Chandra Baily–Borel compactification Borel-de Siebenthal theory Riemann sphere Armand Borel Riemannian geometry Killing form Biholomorphism Hermitian manifold Holomorphic discrete series representation Automorphic form Borel–de Siebenthal theory Polar decomposition Group representation Rosenfeld projective plane Kähler manifold Semisimple Lie group Complex coordinate space Robert Hermann (mathematician) Skew-symmetric matrix Slice theorem (differential geometry) Restricted root system Unit ball Hermitian metric Orthogonal symmetric Lie algebra Siegel domain Unit disk Jordan pair Jordan triple system Transformation group Harish Chandra Parabolic subgroup Levi factor Cauchy integral formula Cayley algebra Cayley projective plane Almost complex structure Generalized flag manifold Complex vector space

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