Rigidity for Einstein manifolds under bounded covering geometry
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908559483076608 |
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| author | Si, Cuifang Xu, Shicheng |
| author_facet | Si, Cuifang Xu, Shicheng |
| contents | In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=λg$ for some real number $λ$. (2) A compact Einstein manifolds with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity for Einstein manifolds under bounded covering geometry Si, Cuifang Xu, Shicheng Differential Geometry 53C23, 53C21, 53C20, 53C24 In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=λg$ for some real number $λ$. (2) A compact Einstein manifolds with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form. |
| title | Rigidity for Einstein manifolds under bounded covering geometry |
| topic | Differential Geometry 53C23, 53C21, 53C20, 53C24 |
| url | https://arxiv.org/abs/2409.15707 |