On the holomorphic torus-Bott tower of aspherical manifolds

We introduce a notion of holomorphic torus-Bott tower which is an iterated holomorphic Seifert fiber space with fiber a complex torus. This is thought of as a holomorphic version of a real Bott tower. The top space of the holomorphic torus-Bott tower is called a holomorphic torus-Bott manifold. We discuss the structure of holomorphic torus-Bott manifolds and particularly the holomorphic rigidity of holomorphic torus-Bott manifolds.