On the Classification of Vaisman Manifolds with Vanishing First Basic Chern Class and Large First Betti Number

Lucas H. S. Gomes

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arXiv · 2604.04134

On the Classification of Vaisman Manifolds with Vanishing First Basic Chern Class and Large First Betti Number

Lucas H. S. Gomes

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Abstract

We show that every Vaisman manifold with large first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold. Furthermore, its complex structure is left-invariant, the characteristic foliation is regular, and the associated fibration is given by the Albanese map. Under the additional assumption that the LCK rank is $1$, the Vaisman structure is also left-invariant. We further prove that if all basic harmonic $1$-forms have constant length, then the Vaisman manifold with large first Betti number is diffeomorphic to a Kodaira-Thurston manifold and its complex structure is the standard complex structure. Finally, we discuss the relationship of this condition with transverse geometric formality in this setting.

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BibTeX RIS

Lucas H. S. Gomes. 2026-05-21. On the Classification of Vaisman Manifolds with Vanishing First Basic Chern Class and Large First Betti Number. https://arxiv.org/abs/2604.04134

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