Statistical Submanifolds Equipped with F -Statistical Connections

Esmaeil Peyghan, Leila Nourmohammadifar and Ion Mihai ()
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Esmaeil Peyghan: Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Leila Nourmohammadifar: Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
Ion Mihai: Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 16, 1-28

Abstract: This paper deals with statistical submanifolds and a family of statistical connections on them. The geometric structures such as the second fundamental form, curvatures tensor, mean curvature, statistical Ricci curvature and the relations among them on a statistical submanifold of a statistical manifold equipped with F -statistical connections are examined. The equations of Gauss and Codazzi of F -statistical connections are obtained. Such structures when the statistical submanifolds are conjugate symmetric are discussed. We present a inequality for statistical submanifolds in real space forms with respect to F -statistical connections. Also, we obtain a basic inequality involving statistical Ricci curvature and the squared F -mean curvature of a statistical submanifold of statistical manifolds.

Keywords: statistical submanifolds; F -statistical connections; conjugate symmetric; F -second fundamental forms; F -mean curvature vector fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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