On Bach-flat gradient shrinking Ricci solitons
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arXiv
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| Format: | Preprint |
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2011
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| _version_ | 1866910362312376320 |
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| author | Cao, Huai-Dong Chen, Qiang |
| author_facet | Cao, Huai-Dong Chen, Qiang |
| contents | In this paper, we classify n-dimensional (n>3) 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 $S^3\times R$. More generally, for n>4, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton $R^n$ or the product $N^{n-1}\times R$, where $N^{n-1}$ is Einstein. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1105_3163 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | On Bach-flat gradient shrinking Ricci solitons Cao, Huai-Dong Chen, Qiang Differential Geometry Mathematical Physics In this paper, we classify n-dimensional (n>3) 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 $S^3\times R$. More generally, for n>4, a Bach-flat gradient shrinking Ricci soliton is either Einstein, or a finite quotient of the Gaussian shrinking soliton $R^n$ or the product $N^{n-1}\times R$, where $N^{n-1}$ is Einstein. |
| title | On Bach-flat gradient shrinking Ricci solitons |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/1105.3163 |