Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds
Hisashi Kasuya

TL;DR
This paper proves that certain solvmanifolds and Oeljeklaus-Toma manifolds cannot support Vaisman metrics, highlighting limitations in their geometric structures.
Contribution
It establishes the non-existence of Vaisman metrics on specific solvmanifolds and Oeljeklaus-Toma manifolds, advancing understanding of their complex geometry.
Findings
Vaisman metrics do not exist on some solvmanifolds with left-invariant complex structures
Oeljeklaus-Toma manifolds do not admit Vaisman metrics
Theorem provides new constraints on geometric structures of these manifolds
Abstract
We prove the non-existence of Vaisman metrics on some solvmanifolds with left-invariant complex structures. By this theorem, we show that Oeljeklaus-Toma manifolds does not admit Vaisman metrics.
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