Kähler Manifold

A manifold for which the Exterior Derivative of the Fundamental Form $\Omega$ associated with the given Hermitian metric vanishes, so $d\Omega=0$.

References

Amorós, J. Fundamental Groups of Compact Kähler Manifolds. Providence, RI: Amer. Math. Soc., 1996.

Iyanaga, S. and Kawada, Y. (Eds.). ``Kähler Manifolds.'' §232 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 732-734, 1980.