Ricci generalized pseudo-parallel Kaehlerian submanifolds in complex space forms

Abstract

Let (M) over cap (m)(c) be a complex m-dimensional space form of holomorphic sectional curvature c and M-n be a complex n-dimensional Kaehlerian submanifold of (M) over cap (m) (c). We prove that if M-n is Ricci generalized pseudo-parallel,, then either M-n is totally geodesic, or parallel to h parallel to(2) = -2/3 (LT - 1/2 (n + 2)c), or at some point x of M-n, parallel to h parallel to(2) (x) > -2/3 (L(x)T(x) - 1/2 (n + 2)c).