Inequalities for casorati curvatures of submanifolds in real space forms

By Pan Zhang, Liangdi Zhang. 2014

46 citations recorded by the source corpus.

Abstract Using Oprea’s optimization methods on submanifolds, we give another proof of the inequalities relating the normalized δ-Casoraticurvature δ^$\hat \delta $c(n−1) for submanifolds in real space forms. Also, inequalities relating the normalized δ-Casorati curvature δC(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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b1cbda3bf88decba694f6954a9aa66a74047b57

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In Applied Mathematics

1. Jae Won Lee
2. Chul Woo Lee
3. Gabriel Eduard Vîlcu

In Mathematical Physics

1. Jae Won Lee
2. Chul Woo Lee
3. Gabriel Eduard Vîlcu

Citations in the corpus

• Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms (2017, methodology): “Oprea’s optimization method on submanifolds, see [25], namely by analyzing a suitable constrained extremum problem; see also [19; 23; 26; 27; 29; 36; 37].”