Slant submanifolds of quaternionic space forms

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...

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

A basic inequality of submanifolds in quaternionic space forms

In this article, we establish a sharp inequality involving δ-invariant introduced by Chen for submanifolds in quaternionic space forms of constant quaternionic sectional curvature with arbitrary codimension. Mathematics Subject Classification: 53B25, 53B35.