2025/04/04 by Lucas H. S. Gomes, Gomes, Lucas H. S. · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2504.03557
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.