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

Published 18 Feb 2025 in math.DG and math.CV | (2502.12500v1)

Abstract: We show that for a certain class of solvable Lie groups, if they admit a left-invariant non-Vaisman locally conformally K\"{a}hler 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.

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