Holomorphic maps of compact generalized Hopf manifolds (Q1376485)

The author studies holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). Obviously Hopf manifolds are the simplest examples. A very interesting fact is that these manifolds have a transversally Kählerian foliation. In particular, a holomorphic map between compact generalized Hopf manifolds preserves these foliations, and a compact complex submanifold of a generalized Hopf manifold is a foliated submanifold and hence a generalized Hopf manifold. Finally, holomorphic submersions of compact generalized Hopf manifolds onto complex manifolds are studied.