Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866916155900297216 |
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| author | Cao, Huai-Dong Liu, Tianbo Xie, Junming |
| author_facet | Cao, Huai-Dong Liu, Tianbo Xie, Junming |
| contents | Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $ \limsup_{r\to \infty} R r^2< \infty $), then the Riemann curvature tensor must have at least sub-quadratic decay, namely, $\limsup_{r\to \infty} |Rm| \ \! r^α< \infty$ for any $0<α<2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_13178 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio Cao, Huai-Dong Liu, Tianbo Xie, Junming Differential Geometry 53C25, 53C21, 53E20 Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $ \limsup_{r\to \infty} R r^2< \infty $), then the Riemann curvature tensor must have at least sub-quadratic decay, namely, $\limsup_{r\to \infty} |Rm| \ \! r^α< \infty$ for any $0<α<2$. |
| title | Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio |
| topic | Differential Geometry 53C25, 53C21, 53E20 |
| url | https://arxiv.org/abs/2203.13178 |