Closed generalized Einstein manifolds with radially flat Ricci curvature
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910882155462656 |
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| author | Hwang, Seungsu Santos, Marcio Yun, Gabjin |
| author_facet | Hwang, Seungsu Santos, Marcio Yun, Gabjin |
| contents | In this paper, we show that a closed $n$-dimensional generalized $(λ, n+m)$-Einstein manifold of constant scalar curvature with weakly radially zero Ricci curvature is isometric to either a sphere ${\Bbb S}^n$, or a product ${\Bbb S}^{1} \times Σ^{n-1}$ of a circle with an $(n-1)$-dimensional Einstein manifold of positive Ricci curvature, up to finite cover and rescaling. Furthermore, if we assume $(M, g)$ has positive isotropic curvature, $M$ must be isometric to either a sphere ${\Bbb S}^n$, or a product ${\Bbb S}^{1} \times {\Bbb S}^{n-1}$ of a circle with an $(n-1)$-sphere. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2108_10675 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Closed generalized Einstein manifolds with radially flat Ricci curvature Hwang, Seungsu Santos, Marcio Yun, Gabjin Differential Geometry 53C25, 58E11 In this paper, we show that a closed $n$-dimensional generalized $(λ, n+m)$-Einstein manifold of constant scalar curvature with weakly radially zero Ricci curvature is isometric to either a sphere ${\Bbb S}^n$, or a product ${\Bbb S}^{1} \times Σ^{n-1}$ of a circle with an $(n-1)$-dimensional Einstein manifold of positive Ricci curvature, up to finite cover and rescaling. Furthermore, if we assume $(M, g)$ has positive isotropic curvature, $M$ must be isometric to either a sphere ${\Bbb S}^n$, or a product ${\Bbb S}^{1} \times {\Bbb S}^{n-1}$ of a circle with an $(n-1)$-sphere. |
| title | Closed generalized Einstein manifolds with radially flat Ricci curvature |
| topic | Differential Geometry 53C25, 58E11 |
| url | https://arxiv.org/abs/2108.10675 |