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Inequalities for algebraic Casorati curvatures and their applications. (English) Zbl 1387.53028

Summary: 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 \(\delta\)-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.

MSC:

53B20 Local Riemannian geometry
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