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Bounds for Statistical Curvatures of Submanifolds in Kenmotsu-like Statistical Manifolds

Author

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  • Aliya Naaz Siddiqui

    (Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana, Ambala 133207, India
    These authors contributed equally to this work.)

  • Mohd Danish Siddiqi

    (Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
    These authors contributed equally to this work.)

  • Ali Hussain Alkhaldi

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

Abstract

In this article, we obtain certain bounds for statistical curvatures of submanifolds with any codimension of Kenmotsu-like statistical manifolds. In this context, we construct a class of optimum inequalities for submanifolds in Kenmotsu-like statistical manifolds containing the normalized scalar curvature and the generalized normalized Casorati curvatures. We also define the second fundamental form of those submanifolds that satisfy the equality condition. On Legendrian submanifolds of Kenmotsu-like statistical manifolds, we discuss a conjecture for Wintgen inequality. At the end, some immediate geometric consequences are stated.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:176-:d:719061
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Aliya Naaz Siddiqui & Ali Hussain Alkhaldi & Lamia Saeed Alqahtani, 2022. "Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature," Mathematics, MDPI, vol. 10(10), pages 1-10, May.

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