Slant submanifolds with prescribed scalar curvature into cosymplectic space form

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Inequalities for Generalized Normalized Δ-casorati Curvatures of Slant Submanifolds in Quaternionic Space Forms

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

A Geometric Inequality for Warped Product Semi-slant Submanifolds of Nearly Cosymplectic Manifolds

Recently, we have shown that there do not exist warped product semi-slant submanifolds of cosymplectic manifolds [K.A. Khan, V.A. Khan and Siraj Uddin, Balkan J. Geom. Appl. 13 (2008), 55–65]. The nearly cosymplectic structure generalizes the cosymplectic one. Therefore the nearly Kaehler structure generalizes the Kaehler structure in almost Hermitian setting. It is interesting that the warped ...

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.

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...