NON-INVARIANT HYPERSURFACES OF A (ε,δ)-TRANS SASAKIAN MANIFOLDS

Abstract

The object of this paper is to study non-invariant hypersurface of a (ε,δ)-trans Sasakian manifolds equipped with (f,g,u,v,λ)-structure. Some properties obeyed by this structure are obtained. The necessary and sufficient conditions also have been obtained for totally umbilical non-invariant hypersurface with (f, g, u, v, λ)-structure of a (ε, δ)-trans Sasakian manifolds to be totally geodesic. The second fundamental form of a non-invariant hypersurface of a (ε, δ)-trans Sasakian manifolds with (f, g, u, v, λ)-structure has been traced under the condition when f is parallel.