Conformal product structures on compact Einstein manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916683859361792 |
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| author | Moroianu, Andrei Pilca, Mihaela |
| author_facet | Moroianu, Andrei Pilca, Mihaela |
| contents | In this note we generalize our previous result, stating that if $(M_1,g_1)$ and $(M_2,g_2)$ are compact Riemannian manifolds, then any Einstein metric on the product $M:=M_1\times M_2$ of the form $g=e^{2f_1}g_1+e^{2f_2}g_2$, with $f_1\in C^\infty(M_2)$ and $f_2\in C^\infty(M_1\times M_2)$, is a warped product metric. Namely, we show that the same conclusion holds if we replace the assumption that the manifold $M$ is globally the product of two compact manifolds by the weaker assumption that $M$ is compact and carries a conformal product structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal product structures on compact Einstein manifolds Moroianu, Andrei Pilca, Mihaela Differential Geometry In this note we generalize our previous result, stating that if $(M_1,g_1)$ and $(M_2,g_2)$ are compact Riemannian manifolds, then any Einstein metric on the product $M:=M_1\times M_2$ of the form $g=e^{2f_1}g_1+e^{2f_2}g_2$, with $f_1\in C^\infty(M_2)$ and $f_2\in C^\infty(M_1\times M_2)$, is a warped product metric. Namely, we show that the same conclusion holds if we replace the assumption that the manifold $M$ is globally the product of two compact manifolds by the weaker assumption that $M$ is compact and carries a conformal product structure. |
| title | Conformal product structures on compact Einstein manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.07886 |