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

摘要

In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of constant ? -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.