*Published Paper*

**Inserted:** 19 jan 2022

**Last Updated:** 19 dec 2023

**Journal:** Publicacions MatemÃ tiques

**Volume:** 68

**Number:** 1

**Pages:** 219â€“239

**Year:** 2024

**Doi:** 10.5565/PUBLMAT6812409

**Abstract:**

We study metric and cohomological properties of Oeljeklaus-Toma manifolds. In particular, we describe the structure of the double complex of differential forms and its Bott-Chern cohomology and we characterize the existence of pluriclosed (aka SKT) metrics in number-theoretic and cohomological terms. Moreover, we prove they do not admit any Hermitian metric $\omega$ such that $\partial \overline{\partial} \omega^k=0$, for $2 \leq k \leq n-2$ and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.

**Tags:**
PRIN2017-MFDS