On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910362395213824 |
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| author | Cao, Huai-Dong Yu, Jiangtao |
| author_facet | Cao, Huai-Dong Yu, Jiangtao |
| contents | In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete noncompact gradient steady Ricci soliton with vanishing $D$-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_13334 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor Cao, Huai-Dong Yu, Jiangtao Differential Geometry 53C21 In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete noncompact gradient steady Ricci soliton with vanishing $D$-tensor is either Ricci-flat, or isometric to the Bryant soliton. Furthermore, the proof extends to the shrinking case and the expanding case as well. |
| title | On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor |
| topic | Differential Geometry 53C21 |
| url | https://arxiv.org/abs/2012.13334 |