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arXiv · 1306.0138

LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem

Victor Vuletescu
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Abstract

A locally conformally K\"ahler (LCK) manifold is a manifold which is covered by a K\"ahler 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 Oeljeklaus-Toma manifold associated to number fields with $2t$ complex embeddings and $s$ real embeddings with $s<t$ there is no LCK metric.

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Victor Vuletescu. 2013-06-01. LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem. https://arxiv.org/abs/1306.0138

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