Hyperbolic manifolds admitting holomorphic fiberings

We give a simple proof of the result that if the total space of a holomorphic fiber bundle is (complete) hyperbolic then both the fiber and the base manifold must be (complete) hyperbolic. Shoshichi Kobayashi tried to set up examples where the total space is hyperbolic but the base is not; our theorem shows that any such example is bound to fail.

On the Automorphism Group of a Holomorphic Fiber Bundle over A Complex Space

In [8], A. Morimoto proved that the automorphism group of a holomorphic principal fiber bundle over a compact complex manifold has a structure of a complex Lie group with the compact-open topology. The purpose of this paper is to get similar results on the automorphism groups of more general types of locally trivial fiber spaces over complex spaces. We study automorphisms of a holomorphic fiber bundle over a complex space which has a complex space Y as the fiber and a (not necessarily complex Lie) group G of holomorphic automorphisms of Y as the structure group (see Definition 3. l).

On Complex Homogeneous Manifolds

Compact complex homogeneous manifolds have been studied in great detail by Borel, Goto, Remmert and Wang (cf., (13)): it was shown that every compact, connected complex homogeneous manifold M is a holomorphic fiber bundle over a projective algebraic homogeneous manifold B with a connected, complex parallelizable fiber F.