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Kähler manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures; a complex structure, a Riemannian structure, and a symplectic structure. On a Kähler manifold ''X'' there exists Kähler potential and the Levi-Civita connection corresponding to the metric of ''X'' gives rise to a connection on the canonical line bundle.
Smooth projective algebraic varieties are examples of Kähler manifolds. By Kodaira embedding theorem, Kähler manifolds that have a positive line bundle can always be embedded into projective spaces.
They are named after German mathematician Erich Kähler.
==Definitions==
Since Kähler manifolds are naturally equipped with several compatible structures, there are many equivalent ways of creating Kähler forms.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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