Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Bang-Yen Chen; Simona Decu; Gabriel-Eduard Vîlcu

doi:10.3390/e23111399

Inequalities for the Casorati Curvature of Totally Real Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Entropy (Basel). 2021 Oct 25;23(11):1399. doi: 10.3390/e23111399.

Authors

Bang-Yen Chen¹, Simona Decu^{2

3}, Gabriel-Eduard Vîlcu^{4

5}

Affiliations

¹ Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA.
² Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania.
³ Romanian Academy, Costin C. Kiriţescu National Institute of Economic Research, Centre of Mountain Economy (CE-MONT), 13 Calea 13 Septembrie, 030508 Bucharest, Romania.
⁴ Faculty of Mathematics and Computer Science, Research Center in Geometry, Topology and Algebra, University of Bucharest, Str. Academiei 14, Sector 1, 70109 Bucharest, Romania.
⁵ Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680 Ploieşti, Romania.

Abstract

The purpose of this article is to establish some inequalities concerning the normalized δ-Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of totally real spacelike submanifolds in statistical manifolds of the type para-Kähler space form. Moreover, this study is focused on the equality cases in these inequalities. Some examples are also provided.

Keywords: Casorati curvature; statistical manifold of type para-Kähler space form; totally real submanifold.