Abstract:

We shall prove that a compact locally homogeneous aspherical Kӓhler manifold   is holomorphically isometric to a quotient of the product by a discrete subgroup which becomes a holomorphic toral bundle over a Hermitian symmetric orbifold . The isometry classification on reduces to that of holomorphic isometric actions of on , while admits a group extension of a Bieberbach group by the product of a Mostow rigidity group and a surface group. The Seifert rigidity applies to show is always smoothly rigid.