Kähler form

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The fundamental form of a Kähler metric on a complex manifold. A Kähler form is a harmonic real differential form of type . A differential form on a complex manifold is the Kähler form of a Kähler metric if and only if every point has a neighbourhood in which

where is a strictly plurisubharmonic function in and are complex local coordinates.

A Kähler form is called a Hodge form if it corresponds to a Hodge metric, i.e. if it has integral periods or, equivalently, defines an integral cohomology class.


[1] R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)


For fundamental form of a Kähler metric see Kähler metric.


[a1] A. Weil, "Introduction à l'Aeetude des variétés kahlériennes" , Hermann (1958)
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Kähler form. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article