Simona Decu (Marinescu)
The Bucharest University of Economic Studies, Bucharest, Romania

We present some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized $\delta$-Casorati curvatures and scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant $\phi$-sectional curvature, endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We point out also an illustrative example. This talk is based on a joint work with Gabriel Vîlcu.

[1] S. Decu, G. E. Vîlcu, Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant $\phi$-Sectional Curvature with Semi-Symmetric Metric Connection, Entropy 24 (6), 2022.
[2] S. Decu, S. Haesen, L. Verstraelen, G. E. Vîlcu, Curvature invariants of statistical submanifolds in Kenmotsu statistical manifolds of constant $\phi$-sectional curvature, Entropy 20, 2018.
[3] S. Decu, S. Haesen, L. Verstraelen, Optimal inequalities characterising quasi-umbilical submanifolds, J. Inequal. Pure Appl. Math. 2008.