Levi's problem for complex homogeneous manifolds

Abstract

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup. Then there exists a closed complex subgroup $J$ of $G$ containing $H$ such that the fibration $\pi :G/H\to G/J$ is the holomorphic reduction of $G/H$, i.e., $G/J$ is holomorphically separable and $\mathcal{O}(G/H)\cong {\pi }^{\ast }\mathcal{O}(G/J)$. In this paper we prove that if $G/H$ is pseudoconvex, i.e., if $G/H$ admits a continuous plurisubharmonic exhaustion function, then $G/J$ is Stein and $J/H$ has no non--constant holomorphic functions.

arguments in section 3 have been changed

References in corpus (1)

• Pseudoconvex domains spread over complex homogeneous manifolds