Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature

Entropy (Basel). 2018 Jul 14;20(7):529. doi: 10.3390/e20070529.


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.

Keywords: Kenmotsu statistical manifold; casorati curvature; dual connections; statistical submanifold.