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Inequalities for Casorati curvatures of submanifolds in real space forms

By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized $δ-$Casorati curvature $\hatδ_c(n-1)$ for submanifolds in real space forms. Also, inequalities relating the normalized $δ-$Casorati curvature $δ_C(n-1)$ 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.

preprint2016arXivOpen access
Pan ZhangLiang Zhang
math.DG
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Pan ZhangLiang Zhang

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