Optimizations on Statistical Hypersurfaces with Casorati Curvatures
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Authors: A. N. SIDDIQUI AND M. H. SHAHID
DOI: 10.46793/KgJMat2103.449S
Abstract:
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 δ−Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.
Keywords:
δ−Casorati curvatures, holomorphic statistical manifold, statistical hypersurfaces, normalized scalar curvature, dual connections.
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