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

2013/06/01 by Vuletescu, Victor
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.0138

Abstract

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 Oeljeklaus-Toma manifold associated to number fields with 2t complex embeddings and s real embeddings with s

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