Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (3): 1239-1244.doi: 10.1016/S0252-9602(12)60095-2

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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.

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

CLC Number: 

  • 53C21
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