On locally conformally Kahler metrics on Oeljeklaus-Toma manifolds

We show that Oeljeklaus-Toma manifolds X (K, U) where K is a number field of signature (s, t) such that s >= 1, t >= 2 and s >= 2t admit no locally conformally Kahler metric. Combined with the earlier results by Dubickas (N Y J Math 20:257-274, 2014) and Oeljeklaus and Toma (Ann Inst Fourier Grenoble 55(1):161-171, 2005) this completely solves the problem of existence of locally conformally Uhler metrics on Oeljeklaus-Toma manifolds.

Automated summary

We prove that Oeljeklaus-Toma manifolds X (K, U) with certain conditions do not admit any locally conformally Kahler metric, which completely solves the problem of existence of locally conformally Uhler metrics on these manifolds, in combination with earlier works by Dubickas and Oeljeklauss and Toma.