数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1239-1244.doi: 10.1016/S0252-9602(12)60095-2

• 论文 • 上一篇    下一篇

ON THE KÄ|HLER-RICCI SOLITONS WITH VANISHING BOCHNER-WEYL TENSOR

苏延辉1|张坤2   

  1. 1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    2. Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • 收稿日期:2010-12-12 修回日期:2011-02-16 出版日期:2012-05-20 发布日期:2012-05-20
  • 基金资助:

    This work is supported by the National Natural Science Foundation of China under the grant numbers 11126073, and the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017.

ON THE KÄ|HLER-RICCI SOLITONS WITH VANISHING BOCHNER-WEYL TENSOR

 SU Yan-Hui1, ZHANG Kun2   

  1. 1. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    2. Department of Mathematics, South China University of Technology, Guangzhou 510640, China
  • Received:2010-12-12 Revised:2011-02-16 Online:2012-05-20 Published:2012-05-20
  • Supported by:

    This work is supported by the National Natural Science Foundation of China under the grant numbers 11126073, and the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017.

摘要:

In this article, we study the steady, shrinking, and expanding Kähler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.

关键词: Ricci flow, Kahler Ricci soliton, Bochner-Weyl tensor

Abstract:

In this article, we study the steady, shrinking, and expanding Kähler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.

Key words: Ricci flow, Kahler Ricci soliton, Bochner-Weyl tensor

中图分类号: 

  • 53C21