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Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature
Simona Decu1,2, Stefan Haesen3,4, Leopold Verstraelen5
1Department of Applied Mathematics, Bucharest University of Economic Studies, Piaţa Romană 6, 010374 Bucharest, Romania.
Abstract:
In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties. We establish some inequalities involving the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant). Moreover, we prove that the equality cases of the inequalities hold if and only if the imbedding curvature tensors h and h∗ of the submanifold (associated with the dual connections) satisfy h=-h∗, i.e., the submanifold is totally geodesic with respect to the Levi-Civita connection.
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