Contact CR-submanifolds with parallel mean curvature vector of a Sasakian 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...

Contact CR Submanifolds of maximal Contact CR dimension of Sasakian Space Form

In this paper, we investigate contact CR submanifolds of contact CR dimension in Sasakian space form and introduce the general structure of these submanifolds and then studying structures of this submanifols with the condition  h(FX,Y)+h(X,FY)=g(FX,Y)zeta, for the normal vector field zeta, which is nonzero, and we classify these submanifolds.

Contact CR-warped product submanifolds in generalized Sasakian Space Forms

In [4] B. Y. Chen studied warped product CR-submanifolds in Kaehler manifolds. Afterward, I. Hasegawa and I. Mihai [5] obtained a sharp inequality for the squared norm of the second fundamental form for contact CR-warped products in Sasakian space form. Recently Alegre, Blair and Carriago [1] introduced generalized Sasakian space form. The aim of present paper is to study contact CR-warped prod...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Submanifolds with Parallel Mean Curvature Vector in Pinched Riemannian Manifolds

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.