ON AN INVARIANT SUBMANIFOLD OF HYPERBOLIC SASAKIAN MANIFOLDS

The object of the present paper is to study an invariant submanifold of hyperbolic Sasakian maifolds. In this paper, we consider semiparallel and 2-semiparallel invariant submanifolds of hyperbolic Sasakian manifold and it is shown that these submanifolds are totally geodesic. It is also proved that on an invariant submanifold of hyperbolic Sasakian manifolds the conditions $I(X, Y).\alpha = 0$, $I(X, Y).\tilde{\nabla}\alpha = 0$, $C(X, Y).\alpha = 0$, $C(X, Y).\tilde{nabla}\alpha = 0$ holds if and only if it is totally geodesic.