On metric and cohomological properties of Oeljeklaus-Toma manifolds

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 $2\le k\le n-2$ and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.

arXiv commentFinal version, to appear in Publicacions Matemàtiques

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