Parallel vector fields on the noninvariant hypersurface of a Sasakian   manifold
  In 1970, Samuel I. Goldberg and Kentaro Yano defined the notion of noninvariant hypersurface of a Sasakian manifold [1]. In this paper we have studied the properties of parallel vector fields with respect to induced connection on the noninvariant hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(\phi, g, u, v, \lambda)-$ structure and proved that if the vector field $V$ is parallel with respect to induced connection on $M$ then $M$ is totally geodesic. 
Sachin Kumar Srivastava, Alok Kumar Srivastava and Dhruwa Narain
math.DG