Non Invariant Hypersurfaces of Quasi Sasakian Manifolds

Abstract

The aim of the present paper is to study noninvariant hypersurfaces of a quasi sasakian manifold with  structure. We have broken the paper into some parts. The first part contains the properties of this structure. In the second part the second fundamental form of noninvariant hypersurfaces of quasi sasakian manifolds with structure have been calculated provided that f is parallel . Third part is mainly based on non invariant hypersurface with structure and totally geodesic submanifold of quasi sasakian manifolds. Finaly  we conclude the paper by obtaining the necessary condition for totally geodesic or totally umbilical noninvariant hypersurfaces with  structure of a quasi sasakian manifold.