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