Remarks on potential functions of noncompact quasi-Einstein manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911311338668032 |
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| author | Gonçalves, Jaciane |
| author_facet | Gonçalves, Jaciane |
| contents | In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on potential functions of noncompact quasi-Einstein manifolds Gonçalves, Jaciane Differential Geometry In this article, we study the set of potential functions on noncompact quasi-Einstein manifolds. We show that the space of all positive potential functions on a three-dimensional noncompact quasi-Einstein manifold has dimension at most two, and that equality holds if and only if the manifold is isometric to a product $B\times\mathbb{R}$, where $B$ is a $λ$-Einstein surface or one of the examples obtained by L. Berard Bergery and described in Besse's book. Moreover, we prove that any asymptotically flat $n$-dimensional quasi-Einstein manifold with $λ=0$ is necessarily Ricci-flat. |
| title | Remarks on potential functions of noncompact quasi-Einstein manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.09653 |