Selfdual geometry of generalized Kählerian manifolds

A complete classification has been obtained of selfdual generalized Kählerian manifolds (of both classical type and nonexceptional Kählerian manifolds of hyperbolic type) of constant scalar curvature. It has also been shown that a generalized Kählerian manifold is anti-selfdual if and only if its scalar curvature vanishes identically. These results essentially generalize well-known results of Hitchin, Bourguignon, Derdziński, Chen, and Itoh.