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单词 KahlerManifold
释义

Kähler manifold


Let M be a complex manifold with integrable complex structureMathworldPlanetmath (http://planetmath.org/AlmostComplexStructure) J.

Suppose M is also a Riemannian manifoldMathworldPlanetmath with metric tensor g such that X,Yg(X,Y)=g(JX,JY). We say that g is an Hermitian metric tensor.

A differentiable manifold M is said to be a Kähler manifold iff all the following conditions are verified:

  • M is a complex manifold with complex structure J

  • M is a Riemannian manifold with an Hermitian metric g

  • J is covariantly constant with regard to the Levi-Civita connectionMathworldPlanetmath (J=0)

Kähler manifolds are symplectic in a natural way with symplectic formMathworldPlanetmath defined by ω(X,Y)=g(JX,Y)

TitleKähler manifold
Canonical nameKahlerManifold
Date of creation2013-03-22 15:43:26
Last modified on2013-03-22 15:43:26
Ownercvalente (11260)
Last modified bycvalente (11260)
Numerical id13
Authorcvalente (11260)
Entry typeDefinition
Classificationmsc 53D99
Synonymkählerian manifold
Synonymkähler structure
Related topicalmostcomplexstructure
Related topicRiemannianMetric
Related topicHyperkahlerManifold
Related topicMathbbCIsAKahlerManifold
Related topicSymplecticManifold
Related topicaKahlerManifoldIsSymplectic
Related topicAKahlerManifoldIsSymplectic
Related topicAlmostComplexStructure
DefinesHermitian metric tensor
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