Vaisman metrics on solvmanifolds and $d_{\theta}$-cohomology
  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. 
Hisashi Kasuya
math.CV math.DG