Bach-flat gradient steady Ricci solitons
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2011
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| _version_ | 1866910362334396416 |
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| author | Cao, Huai-Dong Catino, Giovanni Chen, Qiang Mantegazza, Carlo Mazzieri, Lorenzo |
| author_facet | Cao, Huai-Dong Catino, Giovanni Chen, Qiang Mantegazza, Carlo Mazzieri, Lorenzo |
| contents | In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in [6] and [9]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1107_4591 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Bach-flat gradient steady Ricci solitons Cao, Huai-Dong Catino, Giovanni Chen, Qiang Mantegazza, Carlo Mazzieri, Lorenzo Differential Geometry In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in [6] and [9]. |
| title | Bach-flat gradient steady Ricci solitons |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1107.4591 |