IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v52y2021i2d10.1007_s13226-021-00034-7.html
   My bibliography  Save this article

Compact gradient $$\rho$$ ρ -Einstein soliton is isometric to the Euclidean sphere

Author

Listed:
  • Absos Ali Shaikh

    (The University of Burdwan, Golapbag)

  • Chandan Kumar Mondal

    (The University of Burdwan, Golapbag
    Netaji Subhas Open University)

  • Prosenjit Mandal

    (The University of Burdwan, Golapbag)

Abstract

In this paper, we have investigated some aspects of gradient $$\rho$$ ρ -Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient $$\rho$$ ρ -Einstein soliton satisfying some curvature conditions is isometric to the Euclidean sphere by showing that the scalar curvature becomes constant. Second, we have shown that in a non-compact gradient $$\rho$$ ρ -Einstein soliton satisfying an integral condition, the scalar curvature vanishes.

Suggested Citation

  • Absos Ali Shaikh & Chandan Kumar Mondal & Prosenjit Mandal, 2021. "Compact gradient $$\rho$$ ρ -Einstein soliton is isometric to the Euclidean sphere," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 335-339, June.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00034-7
    DOI: 10.1007/s13226-021-00034-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-021-00034-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-021-00034-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00034-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.