ON Bach-flat Gradient Shrinking Ricci Solitons

Huai-Dong Cao Lehigh University Qiang Chen Lehigh University

Differential Geometry mathscidoc:1703.10006

Duke Math. J. , 162, (6), 1149–1169, 2013
In this paper, we classify n-dimensional ($n\ge 4$) complete Bach-flat gradient shrinking Ricci solitons. More precisely, we prove that any 4-dimensional Bach-flat gradient shrinking Ricci soliton is either Einstein, or locally conformally flat hence a finite quotient of the Gaussian shrinking soliton R^4 or the round cylinder S^3 x R. More generally, for $n\ge 5$, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton $R^n$ or the product $N^{n-1}xR$, where $N^{n-1}$ is Einstein.
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@inproceedings{huai-dong2013on,
  title={ON Bach-flat Gradient Shrinking Ricci Solitons},
  author={Huai-Dong Cao, and Qiang Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313110051106859664},
  booktitle={Duke Math. J. },
  volume={162},
  number={6},
  pages={1149–1169},
  year={2013},
}
Huai-Dong Cao, and Qiang Chen. ON Bach-flat Gradient Shrinking Ricci Solitons. 2013. Vol. 162. In Duke Math. J. . pp.1149–1169. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170313110051106859664.
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