Invariant Submanifolds of (€ )-Sasakian Manifolds.

n this paper, we consider invariant submanifolds of an (€)-Sasakian manifolds. We show that if the second fundamental form of an invariant submanifold of a (€)-Sasakian manifold is recurrent then the submanifold is totally geodesic. We also prove that, invariant submanifolds of an Einstein (€)-Sasakian manifolds satisfying the conditions C(X, Y ) · σ = 0 and C(X, Y ) · ∇σ = 0 with €r ≠ n(n − 1) are also totally geodesic. [ABSTRACT FROM AUTHOR]