Complex immersions in Kahler manifolds of positive holomorphic k-Ricci curvature

The main purpose of this paper is to prove several connectedness theorems for complex immersions of closed manifolds in Kahler manifolds with positive holomorphic k-Ricci curvature. In particular this generalizes the classical Lefschetz hyperplane section theorem for projective varieties. As an immediate geometric application we prove that a complex immersion of an n-dimensional closed manifold in a simply connected closed Kahler m-manifold M with positive holomorphic k-Ricci curvature is an embedding, provided that 2n >= m+ k. This assertion for k = 1 follows from the Fulton-Hansen theorem ( 1979).