Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds

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.