  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.
