Optimizations on Statistical Hypersurfaces with Casorati Curvatures

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DOI: 10.46793/KgJMat2103.449S


In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature k is bounded above by the generalized normalized δCasorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.


δCasorati curvatures, holomorphic statistical manifold, statistical hypersurfaces, normalized scalar curvature, dual connections.


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