B.y. Chen Inequalities for Bi-slant Submanifolds in Generalized Complex 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...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Ideal Slant Submanifolds in Complex Space Forms

Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. Recently, B.-Y. Chen studied Lagrangian submanifolds in complex space forms which are ideal. He proved that such submanifolds are minimal. He also classified ideal Lagrangian submani...

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.

Warped Product Submanifolds in Generalized Complex Space Forms

B.Y. Chen [5] established a sharp inequality for the warping function of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. Later, in [4], he studied warped product submanifolds in complex hyperbolic spaces. In the present paper, we establish an inequality between the warping function f (intrinsic structure) and the squared mean curvature ‖H‖2 and th...