Four-dimensional complete gradient shrinking Ricci solitons
| Autor: | Cao, Huai-Dong, Ribeiro Jr, Ernani, Zhou, Detang |
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| Rok vydání: | 2020 |
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| Zdroj: | J. Reine Angew. Math. 778 (2021), 127-144 |
| Druh dokumentu: | Working Paper |
| Popis: | In this article, we study four-dimensional complete gradient shrinking Ricci solitons. We prove that a four-dimensional complete gradient shrinking Ricci soliton satisfying a pointwise condition involving either the self-dual or anti-self-dual part of the Weyl tensor is either Einstein, or a finite quotient of either the Gaussian shrinking soliton $\Bbb{R}^4,$ or $\Bbb{S}^{3}\times\Bbb{R}$, or $\Bbb{S}^{2}\times\Bbb{R}^{2}.$ In addition, we provide some curvature estimates for four-dimensional complete gradient Ricci solitons assuming that its scalar curvature is suitable bounded by the potential function. Comment: Final Version. To appear in Crelle's Journal (Journal f\"ur die reine und angewandte Mathematik) |
| Databáze: | arXiv |
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