On locally conformally flat manifolds with positive pinched Ricci curvature
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913699839606784 |
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| author | Cheng, Liang |
| author_facet | Cheng, Liang |
| contents | By using the Yamabe flow, we prove that if $(M^n,g)$, $n\geq3$, is an $n$-dimensional locally conformally flat complete Riemannian manifold $Rc\geq εRg>0$, where $ε>0$ is a uniformly constant, then $M^n$ must be compact. Our result shows that Hamilton's pinching conjecture also holds for higher dimensional case if we assume additionally the metric is locally conformally flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06648 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On locally conformally flat manifolds with positive pinched Ricci curvature Cheng, Liang Differential Geometry By using the Yamabe flow, we prove that if $(M^n,g)$, $n\geq3$, is an $n$-dimensional locally conformally flat complete Riemannian manifold $Rc\geq εRg>0$, where $ε>0$ is a uniformly constant, then $M^n$ must be compact. Our result shows that Hamilton's pinching conjecture also holds for higher dimensional case if we assume additionally the metric is locally conformally flat. |
| title | On locally conformally flat manifolds with positive pinched Ricci curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2303.06648 |