Vaisman metrics on solvmanifolds and $d_{\theta}$-cohomology

TL;DR

This paper investigates the existence of Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds, proving their non-existence in certain cases using $d_{ heta}$-cohomology techniques.

Contribution

It establishes new non-existence results for Vaisman metrics on specific classes of solvmanifolds and Oeljeklaus-Toma manifolds.

Findings

Vaisman metrics do not exist on certain solvmanifolds with invariant complex structures.

Oeljeklaus-Toma manifolds with (s,1) admit no Vaisman metric.

The paper employs $d_{ heta}$-cohomology to derive these non-existence results.

Abstract

We prove the non-existence of Vaisman metrics on some solvmanifolds with a left-invariant complex structure. By this theorem, we show that every Oeljeklaus-Toma manifold with $(s,1)$ admits no Vaisman metric.