C-totally real pseudo-parallel submanifolds of S-space forms

Abstract

Let M(c) be a (2n + s)−dimensional S-space form of constant f−sectional curvature c and M be an n-dimensional C-totally real, minimal submanifold of M(c). We prove that if M is pseudo parallel and Ln − 1/4 (n(c + 3s) + c − s) ≥ 0, then M is totally geodesic.