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Statistical Submanifolds Equipped with F -Statistical Connections

Author

Listed:
  • 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)

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.

Suggested Citation

  • Esmaeil Peyghan & Leila Nourmohammadifar & Ion Mihai, 2024. "Statistical Submanifolds Equipped with F -Statistical Connections," Mathematics, MDPI, vol. 12(16), pages 1-28, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2492-:d:1454954
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    References listed on IDEAS

    as
    1. Adela Mihai & Ion Mihai, 2018. "Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature," Mathematics, MDPI, vol. 6(3), pages 1-8, March.
    2. Paul Vos, 1989. "Fundamental equations for statistical submanifolds with applications to the Bartlett correction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 429-450, September.
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