2024 ON METRIC AND COHOMOLOGICAL PROPERTIES OF OELJEKLAUS–TOMA MANIFOLDS
Daniele Angella, Artūras Dubickas, Alexandra Otiman, Jonas Stelzig
Author Affiliations +
Publ. Mat. 68(1): 219-239 (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 that they do not admit any Hermitian metric ω such that ¯ωk=0, for 2kn2, and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus–Toma manifolds admitting pluriclosed metrics.

Funding Statement

The first named author is supported by project PRIN2017 “Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics” (code 2017JZ2SW5), and by GNSAGA of INdAM. The third named author is supported by GNSAGA of INdAM and by a grant of the Ministry of Research and Innovation, CNCS - UEFISCDI, project no. PN-III-P4-ID-PCE-2020-0025, within PNCDI III.

Citation

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Daniele Angella. Artūras Dubickas. Alexandra Otiman. Jonas Stelzig. "ON METRIC AND COHOMOLOGICAL PROPERTIES OF OELJEKLAUS–TOMA MANIFOLDS." Publ. Mat. 68 (1) 219 - 239, 2024. https://doi.org/10.5565/PUBLMAT6812409

Information

Received: 21 January 2022; Accepted: 2 September 2022; Published: 2024
First available in Project Euclid: 25 December 2023

MathSciNet: MR4682729
Digital Object Identifier: 10.5565/PUBLMAT6812409

Subjects:
Primary: 53C55 , 57T15

Keywords: Bott–Chern cohomology , Cohomology , Hermitian metric , Oeljeklaus–Toma manifold , pluriclosed , SKT

Rights: Copyright © 2024 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.68 • No. 1 • 2024
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