Adapted metrics on locally conformally product manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913623924801536 |
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| author | Moroianu, Andrei Pilca, Mihaela |
| author_facet | Moroianu, Andrei Pilca, Mihaela |
| contents | We show that the Gauduchon metric $g_0$ of a compact locally conformally product manifold $(M,c,D)$ of dimension greater than $2$ is adapted, in the sense that the Lee form of $D$ with respect to $g_0$ vanishes on the $D$-flat distribution of $M$. We also characterize adapted metrics as critical points of a natural functional defined on the conformal class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00185 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adapted metrics on locally conformally product manifolds Moroianu, Andrei Pilca, Mihaela Differential Geometry We show that the Gauduchon metric $g_0$ of a compact locally conformally product manifold $(M,c,D)$ of dimension greater than $2$ is adapted, in the sense that the Lee form of $D$ with respect to $g_0$ vanishes on the $D$-flat distribution of $M$. We also characterize adapted metrics as critical points of a natural functional defined on the conformal class. |
| title | Adapted metrics on locally conformally product manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2305.00185 |