Victor Vuletescu: LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem, p.225-231


A locally conformally Kähler (LCK) manifold is a manifold which is covered by a Kähler manifold, with the deck transform group acting by homotheties. We show that the search for LCK metrics on Oeljeklaus-Toma manifolds leads to a (yet another) variation on Kronecker's theorem on units. In turn, this implies that on any Oeljeklaus-Toma manifold associated to a number field with $2t$ complex embeddings and $s$ real embeddings with $1<s\leq t$ there is no LCK metric.

Key Words: Locally conformally Kähler manifold, number field, units.

2000 Mathematics Subject Classification: Primary: 11R27;
Secondary: 53C55.

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