IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i19p3132-d1493413.html
   My bibliography  Save this article

Continuity Equation of Transverse Kähler Metrics on Sasakian Manifolds

Author

Listed:
  • Yushuang Fan

    (Mathematical College, China University of Geosciences (Beijing), Beijing 100083, China)

  • Tao Zheng

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

We introduce the continuity equation of transverse Kähler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normalized) continuity equation converges smoothly to the unique η -Einstein metric in the basic Bott–Chern cohomological class of the initial transverse Kähler metric (resp. first basic Chern class). These results are the transverse version of the continuity equation of the Kähler metrics studied by La Nave and Tian, and also counterparts of the Sasaki–Ricci flow studied by Smoczyk, Wang, and Zhang.

Suggested Citation

  • Yushuang Fan & Tao Zheng, 2024. "Continuity Equation of Transverse Kähler Metrics on Sasakian Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-28, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3132-:d:1493413
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/19/3132/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/19/3132/
    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:12:y:2024:i:19:p:3132-:d:1493413. 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.