IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p150-d311411.html
   My bibliography  Save this article

On Differential Equations Characterizing Legendrian Submanifolds of Sasakian Space Forms

Author

Listed:
  • Rifaqat Ali

    (Department of Mathematics, College of Sciences and Arts, Muhayil, King Khalid University, Abha 9004, Saudi Arabia)

  • Fatemah Mofarreh

    (Mathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi Arabia)

  • Nadia Alluhaibi

    (Department of Mathematics, Science and Arts College, Rabigh Campus, King Abdulaziz University, Jeddah 21911, Saudi Arabia)

  • Akram Ali

    (Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia)

  • Iqbal Ahmad

    (College of Engineering, Qassim University, Buraidah 51452, Al-Qassim, Saudi Arabia)

Abstract

In this paper, we give an estimate of the first eigenvalue of the Laplace operator on minimally immersed Legendrian submanifold N n in Sasakian space forms N ˜ 2 n + 1 ( ϵ ) . We prove that a minimal Legendrian submanifolds in a Sasakian space form is isometric to a standard sphere S n if the Ricci curvature satisfies an extrinsic condition which includes a gradient of a function, the constant holomorphic sectional curvature of the ambient space and a dimension of N n . We also obtain a Simons-type inequality for the same ambient space forms N ˜ 2 n + 1 ( ϵ ) .

Suggested Citation

  • Rifaqat Ali & Fatemah Mofarreh & Nadia Alluhaibi & Akram Ali & Iqbal Ahmad, 2020. "On Differential Equations Characterizing Legendrian Submanifolds of Sasakian Space Forms," Mathematics, MDPI, vol. 8(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:150-:d:311411
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/150/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/150/
    Download Restriction: no
    ---><---

    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:8:y:2020:i:2:p:150-:d:311411. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.