A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910176145047552 |
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| author | Wang, Chen Wu, Guoqiang |
| author_facet | Wang, Chen Wu, Guoqiang |
| contents | Let $(M^4, g, f)$ be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \frac{1}{2}g$. If its scalar curvature is $1$, Cheng-Zhou \cite{Cheng-Zhou} proved that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$. In this note we present an alternative proof by analyzing the asymptotic geometry at infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature Wang, Chen Wu, Guoqiang Differential Geometry Analysis of PDEs Let $(M^4, g, f)$ be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \frac{1}{2}g$. If its scalar curvature is $1$, Cheng-Zhou \cite{Cheng-Zhou} proved that it is a finite quotient of $\mathbb{R}^2\times \mathbb{S}^2$. In this note we present an alternative proof by analyzing the asymptotic geometry at infinity. |
| title | A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.26163 |