COMPACT COMPLEX HOMOGENEOUS SPACES WITH SOLVABLE FUNDAMENTAL GROUP

In this paper, complex Lie groups acting transitively and effectively on complex manifolds with solvable (nilpotent) fundamental groups are studied. It is shown that if is nilpotent, then locally , where is semisimple and is nilpotent. In the case when is solvable, the Levi decomposition of the group is direct if and only if the stationary subgroup contains a maximal unipotent subgroup of the semisimple part. The question of the existence of transitive semisimple groups on is considered.