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arXiv · 2504.03557

Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurston Nilmanifolds

Lucas H. S. Gomes
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Abstract

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.

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Lucas H. S. Gomes. 2025-04-04. Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurston Nilmanifolds. https://arxiv.org/abs/2504.03557

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