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Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

Author

Listed:
  • Aliya Naaz Siddiqui

    (Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India)

  • Bang-Yen Chen

    (Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA)

  • Oguzhan Bahadir

    (Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University, Kahrmanmaras 46100, Turkey)

Abstract

Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R × f N 2 and N 1 × f R . Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen’s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi–Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.

Suggested Citation

  • Aliya Naaz Siddiqui & Bang-Yen Chen & Oguzhan Bahadir, 2019. "Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds," Mathematics, MDPI, vol. 7(9), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:797-:d:262857
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    References listed on IDEAS

    as
    1. 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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    Cited by:

    1. Abdullah Ali H. Ahmadini & Mohd. Danish Siddiqi & Aliya Naaz Siddiqui, 2024. "Statistical Solitonic Impact on Submanifolds of Kenmotsu Statistical Manifolds," Mathematics, MDPI, vol. 12(9), pages 1-16, April.
    2. Meraj Ali Khan & Ibrahim Aldayel, 2020. "Ricci Curvature Inequalities for Skew CR-Warped Product Submanifolds in Complex Space Forms," Mathematics, MDPI, vol. 8(8), pages 1-19, August.
    3. Aliya Naaz Siddiqui & Mohd Danish Siddiqi & Ali Hussain Alkhaldi, 2022. "Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds," Mathematics, MDPI, vol. 10(2), pages 1-15, January.

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