# Kähler form

From Encyclopedia of Mathematics

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.

#### References

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

#### Comments

For fundamental form of a Kähler metric see Kähler metric.

#### References

[a1] | A. Weil, "Introduction à l'Aeetude des variétés kahlériennes" , Hermann (1958) |

**How to Cite This Entry:**

Kähler form.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=K%C3%A4hler_form&oldid=23348

This article was adapted from an original article by A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article