Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People's Republic of China ; Departamento de Análise, Universidade Federal Fluminense (UFF), Niterói, 24020-140 RJ Brazil
Abstract:
The main purpose of this paper is to prove several connectedness theorems for complex immersions of closed manifolds in Kähler manifolds with positive holomorphic -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 -dimensional closed manifold in a simply connected closed Kähler -manifold with positive holomorphic -Ricci curvature is an embedding, provided that . This assertion for follows from the Fulton-Hansen theorem (1979).