IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3097-d1193481.html
   My bibliography  Save this article

Characterizations of the Frame Bundle Admitting Metallic Structures on Almost Quadratic ϕ -Manifolds

Author

Listed:
  • Mohammad Nazrul Islam Khan

    (Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia)

  • Uday Chand De

    (Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, India)

  • Teg Alam

    (Department of Industrial Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi Arabia)

Abstract

In this work, we have characterized the frame bundle F M admitting metallic structures on almost quadratic ϕ -manifolds ϕ 2 = p ϕ + q I − q η ⊗ ζ , where p is an arbitrary constant and q is a nonzero constant. The complete lifts of an almost quadratic ϕ -structure to the metallic structure on F M are constructed. We also prove the existence of a metallic structure on F M with the aid of the J ˜ tensor field, which we define. Results for the 2-Form and its derivative are then obtained. Additionally, we derive the expressions of the Nijenhuis tensor of a tensor field J ˜ on F M . Finally, we construct an example of it to finish.

Suggested Citation

  • Mohammad Nazrul Islam Khan & Uday Chand De & Teg Alam, 2023. "Characterizations of the Frame Bundle Admitting Metallic Structures on Almost Quadratic ϕ -Manifolds," Mathematics, MDPI, vol. 11(14), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3097-:d:1193481
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3097/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3097/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
    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. Chi Hongmei, 2013. "Generation of parallel modified Kronecker sequences," Monte Carlo Methods and Applications, De Gruyter, vol. 19(4), pages 261-271, December.
    2. Falcón, Sergio & Plaza, Ángel, 2009. "The metallic ratios as limits of complex valued transformations," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 1-13.
    3. Cristina E. Hretcanu & Mircea Crasmareanu, 2023. "The ( α , p )-Golden Metric Manifolds and Their Submanifolds," Mathematics, MDPI, vol. 11(14), pages 1-13, July.
    4. Özkan, Engin & Kuloǧlu, Bahar & Peters, James F., 2021. "K-Narayana sequence self-Similarity. flip graph views of k-Narayana self-Similarity," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    5. Khan, Mohammad Nazrul Islam, 2021. "Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Falcon, Sergio & Plaza, Ángel, 2009. "k-Fibonacci sequences modulo m," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 497-504.
    7. Cristina E. Hretcanu & Adara M. Blaga, 2021. "Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey," Mathematics, MDPI, vol. 9(19), pages 1-22, October.
    8. Basu, Manjusri & Prasad, Bandhu, 2009. "Coding theory on the m-extension of the Fibonacci p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2522-2530.

    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:11:y:2023:i:14:p:3097-:d:1193481. 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.