GLOBALIZATION OF HOLOMORPHIC ACTIONS ON PRINCIPLE-BUNDLES

Suppose G is a Lie group acting as a group of holomorphic automorphism s on a holomorphic principal bundle P --> X. We show that if there is a holomorphic action of the complexification G(C) of G on X, this lift s to a holomorphic action of G(C) on the bundle P --> X. Two applicati ons are presented. We prove that given any connected homogeneous compl ex manifold G/H with more than one end, the complexification G(C) of G acts holomorphically and transitively on G/H. We also show that the e nds of a homogeneous complex manifold G/H with more than two ends esse ntially come from a space of the form S/Gamma, where Gamma is a Zarisk i dense discrete subgroup of a semisimple complex Lie group S with S a nd Gamma being explicitly constructed in terms of G and H.