Vaisman metrics on solvmanifolds and Oeljeklaus-Toma 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.Comment: 12 page. arXiv admin note: substantial text overlap with arXiv:1104.3451. to appear in Bull. Lond. math. so