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arXiv · 2502.12500

A characterization of Oeljeklaus-Toma manifolds in locally conformally K\"{a}hler geometry

Shuho Kanda
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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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Shuho Kanda. 2025-02-18. A characterization of Oeljeklaus-Toma manifolds in locally conformally K\"{a}hler geometry. https://arxiv.org/abs/2502.12500

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