数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (5): 1235-1239.doi: 10.1007/s10473-019-0503-0

• 论文 • 上一篇    下一篇

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

张珠洪1, 陈志伟2   

  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
  • 收稿日期:2018-08-30 修回日期:2018-11-19 出版日期:2019-10-25 发布日期:2019-11-11
  • 通讯作者: Zhuhong ZHANG E-mail:juhoncheung@sina.com
  • 作者简介:Chih-Wei CHEN,E-mail:BabbageTW@gmail.com,chencw@math.nsysu.edu.tw
  • 基金资助:
    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).

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).

摘要: 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.

关键词: shrinking gradient Ricci solitons, positive Ricci curvature, pinched Weyl tensor

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

中图分类号: 

  • 53C24