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
Affiliations
Bang-Yen Chen
Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA
Simona Decu
Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania
Gabriel-Eduard Vîlcu
Faculty of Mathematics and Computer Science, Research Center in Geometry, Topology and Algebra, University of Bucharest, Str. Academiei 14, Sector 1, 70109 Bucharest, Romania
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.
