D. Angella - A. Dubickas - A. Otiman - J. Stelzig

On metric and cohomological properties of Oeljeklaus-Toma manifolds

Published Paper

Inserted: 19 jan 2022
Last Updated: 19 dec 2023

Journal: Publicacions Matemàtiques
Volume: 68
Number: 1
Pages: 219–239
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