On Locally Conformally K\" ahler metrics on Oeljeklaus-Toma Manifolds

Abstract

We show that Oeljeklaus-Toma manifolds $X(K,U)$ where $K$ is a number field of signature $(s,t)$ such that $s\ge 1,$ $t\ge 2$ and $s\ge 2t$ admit no lck metric. Combined with the earlier results by K. Oeljeklaus - M. Toma and A. Dubickas this completely solves the problem of existence of LCK metrics on Oeljeklaus-Toma manifolds.

Cited by in corpus (1)

• On metric and cohomological properties of Oeljeklaus-Toma manifolds