Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms

Simona Decu and Stefan Haesen
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Simona Decu: Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania
Stefan Haesen: Department of Mathematics, University of Hasselt, BE 3590 Diepenbeek, Belgium

Mathematics, 2022, vol. 10, issue 3, 1-12

Abstract: In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely involving the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms. Furthermore, we investigate the equality cases of these inequalities. As illustrations of the applications of the above inequalities, we consider a few examples.

Keywords: Chen inequality; statistical manifold of type para-Kähler space form; totally real submanifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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