C-Totally real pseudo-parallel submanifolds of Sasakian space forms

Abstract

Let $\widetilde{M}^{2n+1}(c)$ be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature (c) and M n be an n -dimensional C-totally real, minimal submanifold of $\widetilde{M}^{2n+1}(c)$ . We prove that if M n is pseudo-parallel and $Ln-\frac{1}{4}(n(c + 3) + c - 1)\ge 0$ , then M n is totally geodesic.