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

Simona Decu; Gabriel-Eduard Vîlcu

doi:10.3390/e24060800

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

Entropy (Basel). 2022 Jun 8;24(6):800. doi: 10.3390/e24060800.

Authors

Simona Decu^{1

2}, Gabriel-Eduard Vîlcu^{3

4

5}

Affiliations

¹ Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania.
² Romanian Academy, Center of Mountain Economy (CE-MONT), "Costin C. Kiriţescu" National Institute of Economic Research, 13 Calea 13 Septembrie, 030508 Bucharest, Romania.
³ Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania.
⁴ Romanian Academy, "Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania.
⁵ Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania.

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.

Keywords: Casorati curvature; Kenmotsu statistical manifold; semi-symmetric metric connection; statistical manifold.

Grants and funding

This research received no external funding.