Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds

Abstract

The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with (f,g,u,v,λ)-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with (f,g,u,v,λ)-structure have been calculated provided f is parallel. In addition, the eigenvalues of f have been found and proved that a noninvariant hypersurface with (f,g,u,v,λ)-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with (f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold