Hypersurfaces of a Sasakian manifold - revisited

Abstract We study orientable hypersurfaces in a Sasakian manifold. The structure vector field ξ of manifold determines v on hypersurface that is the component Reeb tangential to hypersurface, and it also gives rise smooth function σ namely projection unit normal N . Moreover, we have second tangent given by $\mathbf{u}=-\varphi (N)$ u = − φ ( N ) In this paper, first find necessary sufficient condition for compact be totally umbilical. Then, with assumption u an eigenvector Laplace operator, isometric sphere. It shown converse result holds, provided odd dimensional sphere $\mathbf{S}^{2n+1}$ S 2 n + 1 Similar results are obtained under hypothesis operator. Also, use bound integral Ricci curvature $Ric ( \mathbf{u},\mathbf{u} ) $ R i c , show if