Classification of Kaehler homogeneous manifolds of non-compact dimension two

Abstract

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup such that $X:=G/H$ is Kaehler and the codimension of the top non-vanishing homology group of $X$ with coefficients in ${\mathbb{Z}}_2$ is less than or equal to two. We show that $X$ is biholomorphic to a complex homogeneous manifold constructed using well-known basic building blocks, i.e., $\mathbb{C},{\mathbb{C}}^{\ast }$, Cousin groups, and flag manifolds.

References in corpus (3)

• Cycle Spaces of Flag Domains: A Complex Geometric Viewpoint
• Homogeneous Kähler and Hamiltonian manifolds
• Two Remarks on Kaehler Homogeneous Manifolds