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

Victor Vuletescu

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

Differential Geometry 2013-06-04 v1

Authors: Victor Vuletescu

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.

Keywords

locally conformally Kähler metrics Oeljeklaus-Toma manifolds Kronecker's theorem number fields deck transformations

Cite

@article{arxiv.1306.0138,
  title  = {LCK metrics on Oeljeklaus-Toma manifolds versus Kronecker's theorem},
  author = {Victor Vuletescu},
  journal= {arXiv preprint arXiv:1306.0138},
  year   = {2013}
}

Comments

To appear in Bull. Math. Soc. Sci. Math. Roum., Nouv. Ser

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