On totally umbilical CR-submanifolds of a Kaehler manifold

Abstract

Let M be a compact 3-dimensional totally umbilical CR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector of M does not vanish, then M is either diffeomorphic to S3 or RP3 or a lens space Lp,q3.

Keywords

• CR-submanifolds. totally umbilical submanifolds. Kaehler manifold.