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Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Author

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  • Adela Mihai

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Ion Mihai

    (Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania)

Abstract

We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:3:p:44-:d:136359
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    References listed on IDEAS

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    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. 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.
    2. Simona-Luiza Druta-Romaniuc, 2023. "Quasi-Statistical Schouten–van Kampen Connections on the Tangent Bundle," Mathematics, MDPI, vol. 11(22), pages 1-20, November.
    3. Yanlin Li & M. S. Siddesha & H. Aruna Kumara & M. M. Praveena, 2024. "Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-11, October.
    4. Esmaeil Peyghan & Leila Nourmohammadifar & Ion Mihai, 2024. "Statistical Submanifolds Equipped with F -Statistical Connections," Mathematics, MDPI, vol. 12(16), pages 1-28, August.

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