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arXiv · 2201.06377

On metric and cohomological properties of Oeljeklaus-Toma manifolds

Danielle Angella·Arturas Dubickas·Alexandra Otiman·Jonas Stelzig
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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.

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Danielle Angella, Arturas Dubickas, Alexandra Otiman, Jonas Stelzig. 2022-01-17. On metric and cohomological properties of Oeljeklaus-Toma manifolds. https://doi.org/10.5565/publmat6812409

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