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Inequalities for the Casorati curvatures of slant submanifolds in quaternionic space forms
(Springer International Publishing Ag, 2014) Slesar, Vladimir; Sahin, Bayram; Vilcu, Gabriel-Eduard
In this paper we prove two sharp inequalities that relate the normalized scalar curvature with the Casorati curvature for a slant submanifold in a quaternionic space form. Moreover, we show that in both cases, the equality at all points characterizes the invariantly quasi-umbilical submanifolds.
Optimal Inequalities for Hemi-Slant Riemannian Submersions
(Mdpi, 2022) Akyol, Mehmet Akif; Demir, Ramazan; Poyraz, Nergiz Onen; Vilcu, Gabriel-Eduard
In the present paper, we establish some basic inequalities involving the Ricci and scalar curvature of the vertical and the horizontal distributions for hemi-slant submersions having the total space a complex space form. We also discuss the equality case of the obtained inequalities and provide illustrative examples.