Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

Abstract

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.

The Translation Surfaces on Statistical Manifolds with Normal Distribution

“…In recent years, during literature reviews on statistical submanifolds, it has been observed that studies have focused on Chen inequalities ( [5], [6], [15], [53]),Wintgen inequalities ( [8], [25], [44]) and inequalities involving the normalized δ-Casorati curvatures ( [12], [16], [17], [26], [38], [54]).…”