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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.03557 |
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| _version_ | 1866912763070119936 |
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| author | Gomes, Lucas H. S. |
| author_facet | Gomes, Lucas H. S. |
| contents | We prove that every Vaisman solvmanifold is a finite quotient of a Kodaira-Thurston manifold. More generally, we show that every aspherical compact Vaisman manifold with strongly polycyclic fundamental group is a finite quotient of a Kodaira-Thurston manifold. As consequences, we obtain that every completely solvable solvmanifold admitting a Vaisman structure is a Kodaira-Thurston manifold, that Oeljeklaus-Toma manifolds admit no Vaisman structures (not necessarily left-invariant), and that solvmanifolds does not admit LCK Einstein-Weyl structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurston Nilmanifolds Gomes, Lucas H. S. Differential Geometry We prove that every Vaisman solvmanifold is a finite quotient of a Kodaira-Thurston manifold. More generally, we show that every aspherical compact Vaisman manifold with strongly polycyclic fundamental group is a finite quotient of a Kodaira-Thurston manifold. As consequences, we obtain that every completely solvable solvmanifold admitting a Vaisman structure is a Kodaira-Thurston manifold, that Oeljeklaus-Toma manifolds admit no Vaisman structures (not necessarily left-invariant), and that solvmanifolds does not admit LCK Einstein-Weyl structures. |
| title | Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurston Nilmanifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.03557 |