Inequalities for Casorati curvatures of submanifolds in real space forms

2014/08/21 by Pan Zhang, Liang Zhang, Zhang, Pan +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1408.4996

openalex publication_date 2014/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using T. Oprea's optimization methods on submanifolds, we give another proof of the inequalities relating the normalized δ-Casorati curvature δ_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.

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