Inequalities for Casorati curvatures of submanifolds in real space forms

Abstract

By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized $\delta -$Casorati curvature ${\hat{\delta }}_c(n-1)$ for submanifolds in real space forms. Also, inequalities relating the normalized $\delta -$Casorati curvature ${\delta }_C(n-1)$ for submanifolds in real space forms are obtained. Besides, we characterize a kind of Casorati ideal hypersurface of Euclidean 4-space. We also show that this kind of Casorati ideal hypersurface is rigid.

arXiv admin note: text overlap with arXiv:1405.5192 by other authors

References in corpus (3)

• Inequalities for generalized normalized $\delta$-Casorati curvatures of slant submanifolds in quaternionic space forms
• A geometric inequality for warped product semi-slant submanifolds of nearly cosymplectic manifolds
• Classification of ideal submanifolds of real space forms with type number $\le 2$

Cited by in corpus (1)

• Inequalities for algebraic Casorati curvatures and their applications