Improved Chen-ricci Inequality for Lagrangian Submanifolds in Quaternion Space Forms

An Improved Chen-ricci Inequality

Oprea proves that Ric(X) ≤ n−1 4 (c + n||H||) improving the Chen-Ricci inequality for Lagrangian submanifolds in complex space forms by using an optimization technique. In this article, we give an algebraic proof of the inequality and completely classify Lagrangian submanifolds in complex space forms satisfying the equality, which is not discussed in Oprea’s paper.

Ricci Curvature of Quaternion Slant Submanifolds in Quaternion Space Forms

In this article, we obtain sharp estimate of the Ricci curvature of quaternion slant, bi-slant and semi-slant submanifolds in a quaternion space form, in terms of the squared mean curvature.

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

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...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms