Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914165418885120 |
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| author | Cao, Zhongxian |
| author_facet | Cao, Zhongxian |
| contents | Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show that $R$ = $((m-5)k+20)/(m-k+4)λ$ for some $k\in\{0,2,3,4\}$. Both cases of $k=0$ and $k=4$ are already classified. In this paper we will prove that the case $k=3$ is rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature Cao, Zhongxian Differential Geometry Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show that $R$ = $((m-5)k+20)/(m-k+4)λ$ for some $k\in\{0,2,3,4\}$. Both cases of $k=0$ and $k=4$ are already classified. In this paper we will prove that the case $k=3$ is rigid. |
| title | Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.16128 |