hypersurfaces of a sasakian space form with recurrent shape operator

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

Hoph Hypersurfaces of Sasakian Space Form with Parallel Ricci Operator Esmaiel Abedi, Mohammad Ilmakchi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

hypersurfaces with constant mean curvature in a lorentzian space form

Real Hypersurfaces of a Complex Space Form

In this paper, we show that an n-dimensional connected noncompact Ricci soliton isometrically immersed in the ‡at complex space form (C n+1 2 ; J; h; i), with potential vector …eld of the Ricci soliton is the characteristic vector …eld of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the ‡at complex space form (C n+1 2 ; J; h; i) and also obtain a ch...