IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3509-d925670.html
   My bibliography  Save this article

Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection

Author

Listed:
  • Simona Decu

    (Department of Applied Mathematics, Bucharest University of Economic Studies, 6 Piaţa Romană, 010374 Bucharest, Romania
    Center of Mountain Economy (CE-MONT), “Costin C. Kiriţescu” National Institute of Economic Research, Romanian Academy, 13 Calea 13 Septembrie, 030508 Bucharest, Romania)

Abstract

In this paper, we establish some inequalities between the normalized δ -Casorati curvatures and the scalar curvature (i.e., between extrinsic and intrinsic invariants) of spacelike statistical submanifolds in Sasaki-like statistical manifolds, endowed with a semi-symmetric metric connection. Moreover, we study the submanifolds satisfying the equality cases of these inequalities. We also present an appropriate example.

Suggested Citation

  • Simona Decu, 2022. "Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection," Mathematics, MDPI, vol. 10(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3509-:d:925670
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3509/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3509/
    Download Restriction: no
    ---><---

    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.
    2. Simona Decu & Stefan Haesen, 2022. "Chen Inequalities for Spacelike Submanifolds in Statistical Manifolds of Type Para-Kähler Space Forms," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    3. Hülya Aytimur & Adela Mihai & Cihan Özgür, 2021. "Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds," Mathematics, MDPI, vol. 9(11), pages 1-13, June.
    4. Bang-Yen Chen & Adara M. Blaga & Gabriel-Eduard Vîlcu, 2022. "Differential Geometry of Submanifolds in Complex Space Forms Involving δ -Invariants," Mathematics, MDPI, vol. 10(4), pages 1-38, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ion Mihai & Radu-Ioan Mihai, 2022. "General Chen Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
    2. Ion Mihai & Radu-Ioan Mihai, 2021. "A New Algebraic Inequality and Some Applications in Submanifold Theory," Mathematics, MDPI, vol. 9(11), pages 1-10, May.
    3. Chul Woo Lee & Jae Won Lee, 2018. "Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures," Mathematics, MDPI, vol. 6(11), pages 1-10, November.
    4. 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.
    5. 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.
    6. 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.
    7. Vladimir Rovenski, 2022. "Geometric Inequalities for a Submanifold Equipped with Distributions," Mathematics, MDPI, vol. 10(24), pages 1-11, December.
    8. Bang-Yen Chen & Gabriel-Eduard Vîlcu, 2023. "Recent Developments on the First Chen Inequality in Differential Geometry," Mathematics, MDPI, vol. 11(19), pages 1-50, October.
    9. Hülya Aytimur & Mayuko Kon & Adela Mihai & Cihan Özgür & Kazuhiko Takano, 2019. "Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds," Mathematics, MDPI, vol. 7(12), pages 1-19, December.
    10. Oğuzhan Bahadır & Aliya Naaz Siddiqui & Mehmet Gülbahar & Ali Hussain Alkhaldi, 2022. "Main Curvatures Identities on Lightlike Hypersurfaces of Statistical Manifolds and Their Characterizations," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    11. Hülya Aytimur & Adela Mihai & Cihan Özgür, 2021. "Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds," Mathematics, MDPI, vol. 9(11), pages 1-13, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3509-:d:925670. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.