COMPACT HOMOGENEOUS LOCALLY CONFORMALLY KAHLER MANIFOLDS

In this paper we show as main results two structure theorems of a compact homogeneous locally conformally Kahler (or shortly 1.c.K.) manifold, a holomorphic structure theorem asserting that it has a structure of holomorphic principal fiber bundle over a flag manifold with fiber a 1-dimensional complex torus, and a metric structure theorem asserting that it is necessarily of Vaisman type. We also discuss and determine 1.c.K. reductive Lie groups and compact locally homogeneous 1.c.K. manifolds of reductive Lie groups.