The coarse orbit types of non-Kählerian, symplectic homogeneous spaces whose transformation groups are non-compact simple and isotropy subgroups are compact

Abstract

The main purpose of this paper is to determine the coarse orbit types of all non-Kählerian, symplectic homogeneous spaces $G/H$ with $G$ non-compact simple and $H$ compact. Our result, together with the results of Wang and Yichao, enables one to know all dual manifolds of every Kähler $C$-space.