Inequalities for algebraic Casorati curvatures and their applications

2016/07/20 by Mukut Mani Tripathi, Tripathi, Mukut Mani · 1 citation
Mathematics · #53B20 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1607.05828

openalex publication_date 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of different kind of algebraic Casorati curvatures are introduced. Some results expressing basic Casorati inequalities for algebraic Casorati curvatures are presented. Equality cases are also discussed. As a simple application, basic Casorati inequalities for different δ-Casorati curvatures for Riemannian submanifolds are presented. Further applying these results, Casorati inequalities for Riemannian submanifolds of real space forms are obtained. Finally, some problems are presented for further studies.

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