Weakly Einstein hypersurfaces in space forms
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916527648800768 |
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| author | Kim, Jihun Nikolayevsky, Yuri Park, JeongHyeong |
| author_facet | Kim, Jihun Nikolayevsky, Yuri Park, JeongHyeong |
| contents | A Riemannian manifold $(M,g)$ is called \emph{weakly Einstein} if the tensor $R_{iabc}R_{j}^{~~abc}$ is a scalar multiple of the metric tensor $g_{ij}$. We give a complete classification of weakly Einstein hypersurfaces in the spaces of nonzero constant curvature (the classification in a Euclidean space has been previously known). The main result states that such a hypersurface can only be the product of two spaces of constant curvature or a rotation hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly Einstein hypersurfaces in space forms Kim, Jihun Nikolayevsky, Yuri Park, JeongHyeong Differential Geometry 53C25, 53B25 A Riemannian manifold $(M,g)$ is called \emph{weakly Einstein} if the tensor $R_{iabc}R_{j}^{~~abc}$ is a scalar multiple of the metric tensor $g_{ij}$. We give a complete classification of weakly Einstein hypersurfaces in the spaces of nonzero constant curvature (the classification in a Euclidean space has been previously known). The main result states that such a hypersurface can only be the product of two spaces of constant curvature or a rotation hypersurface. |
| title | Weakly Einstein hypersurfaces in space forms |
| topic | Differential Geometry 53C25, 53B25 |
| url | https://arxiv.org/abs/2409.12766 |