On some submanifolds of Kenmotsu manifolds

Abstract

In this paper, we study submanifolds of Kenmotsu manifolds. We prove that if the second fundamental form of a submanifold of a Kenmotsu manifold is recurrent, 2-recurrent or generalized 2-recurrent then the submanifold is totally geodesic. Furthermore, we show that a submanifold of a Kenmotsu manifold with parallel third fundamental form is again totally geodesic. We also consider quasi-umbilical hypersurfaces of Kenmotsu space forms. We show that these type hypersurfaces are generalized quasi-Einstein.