A characterization of Oeljeklaus-Toma manifolds in locally conformally Kähler geometry

We show that for a certain class of solvable Lie groups, if they admit a left-invariant non-Vaisman locally conformally Kähler metric and a lattice, they must arise from the construction of Oeljeklaus-Toma manifolds. This result provides a natural explanation for why number-theoretic considerations play a role in the construction of Oeljeklaus-Toma manifolds.