Invariant submanifolds of (ε)-Sasakian manifolds

Abstract

In this paper, we consider invariant submanifolds of (ε)-Sasakian manifolds. We show that if the second fundamental form of an invariant submanifold of a (ε)-Sasakian manifold is recurrent then the submanifold is totally geodesic. We also prove that invariant submanifolds of Einstein (ε)-Sasakian manifolds satisfying the conditions $C(X, Y)\cdot \sigma = 0$ and $C(X, Y)\cdot \widetilde{\nabla}\sigma = 0$ with $\epsilon r \neq n(n-1)$ are also totally geodesic.