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arXiv · 1408.4996

Inequalities for Casorati curvatures of submanifolds in real space forms

Pan Zhang·Liang Zhang
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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.

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Pan Zhang, Liang Zhang. 2014-08-21. Inequalities for Casorati curvatures of submanifolds in real space forms. https://arxiv.org/abs/1408.4996

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