Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1235-1239.doi: 10.1007/s10473-019-0503-0

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ON SHRINKING GRADIENT RICCI SOLITONS WITH POSITIVE RICCI CURVATURE AND SMALL WEYL TENSOR

Zhuhong ZHANG1, Chih-Wei CHEN2   

  1. 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, China
  • Received:2018-08-30 Revised:2018-11-19 Online:2019-10-25 Published:2019-11-11
  • Contact: Zhuhong ZHANG E-mail:juhoncheung@sina.com
  • Supported by:
    The first author was supported by National Natural Science Foundation of China (11301191). The second author was supported by MOST (MOST107-2115-M-110-007-MY2).

Abstract: We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.

Key words: shrinking gradient Ricci solitons, positive Ricci curvature, pinched Weyl tensor

CLC Number: 

  • 53C24
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