Reducible Riemannian manifolds with conformal product structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918287183446016 |
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| author | Moroianu, Andrei Pilca, Mihaela |
| author_facet | Moroianu, Andrei Pilca, Mihaela |
| contents | We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally isometric to Riemannian manifolds of the form $(M,g)$ with $M=M_1\times M_2\times M_3$ and $g=e^{2f}g_1+g_2+g_3$, where $g_i$ is a Riemannian metric on $M_i$, for $i\in\{1,2,3\}$, and $f\in C^\infty(M_1\times M_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reducible Riemannian manifolds with conformal product structures Moroianu, Andrei Pilca, Mihaela Differential Geometry We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally isometric to Riemannian manifolds of the form $(M,g)$ with $M=M_1\times M_2\times M_3$ and $g=e^{2f}g_1+g_2+g_3$, where $g_i$ is a Riemannian metric on $M_i$, for $i\in\{1,2,3\}$, and $f\in C^\infty(M_1\times M_2)$. |
| title | Reducible Riemannian manifolds with conformal product structures |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.19132 |