Borel’s fixed point theorem for Kaehler manifolds and an application

Abstract:

A short proof of a generalization of the Borel fixed point theorem to the case of Kaehler manifolds is given and, as an application, a short proof of Wang’s theorem that compact simply connected homogeneous manifolds are projective and of the form $G/P$, where $G$ is a complex semisimple Lie group and $P$ is a parabolic subgroup.