Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection

Abstract

In this paper, we establish some inequalities between the normalized δ-Casorati curvatures and the scalar curvature (i.e., between extrinsic and intrinsic invariants) of spacelike statistical submanifolds in Sasaki-like statistical manifolds, endowed with a semi-symmetric metric connection. Moreover, we study the submanifolds satisfying the equality cases of these inequalities. We also present an appropriate example.

Keywords

• statistical manifold
• semi-symmetric metric connection
• Casorati curvature
• Sasaki-like statistical manifold