On metric and cohomological properties of Oeljeklaus-Toma manifolds

Alexandra-Iulia Otiman; Daniele Angella; Arturas Dubickas; Jonas Stelzig

doi:10.5565/PUBLMAT6812409

On metric and cohomological properties of Oeljeklaus-Toma manifolds

Alexandra-Iulia Otiman, Daniele Angella, Arturas Dubickas, Jonas Stelzig

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

We study metric and cohomological properties of Oeljeklaus-Toma manifolds. In particular, we describe the structure of the double complex of dierential 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 [Formula presented], for 2 ≤ k ≤ n - 2, and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.

Original language	English
Journal	Publicacions Matematiques
Volume	68
Issue	1
Pages (from-to)	219-239
ISSN	0214-1493
DOIs	https://doi.org/10.5565/PUBLMAT6812409
Publication status	Published - 2024
Externally published	Yes

Keywords

Bott-Chern cohomology
Hermitian metric
Oeljeklaus-Toma manifold
SKT
cohomology
pluriclosed

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10.5565/PUBLMAT6812409

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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 dierential 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 [Formula presented], for 2 ≤ k ≤ n - 2, and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.",

keywords = "Bott-Chern cohomology, Hermitian metric, Oeljeklaus-Toma manifold, SKT, cohomology, pluriclosed",

author = "Alexandra-Iulia Otiman and Daniele Angella and Arturas Dubickas and Jonas Stelzig",

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doi = "10.5565/PUBLMAT6812409",

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T1 - On metric and cohomological properties of Oeljeklaus-Toma manifolds

AU - Otiman, Alexandra-Iulia

AU - Angella, Daniele

AU - Dubickas, Arturas

AU - Stelzig, Jonas

PY - 2024

Y1 - 2024

N2 - We study metric and cohomological properties of Oeljeklaus-Toma manifolds. In particular, we describe the structure of the double complex of dierential 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 [Formula presented], for 2 ≤ k ≤ n - 2, and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.

AB - We study metric and cohomological properties of Oeljeklaus-Toma manifolds. In particular, we describe the structure of the double complex of dierential 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 [Formula presented], for 2 ≤ k ≤ n - 2, and we give explicit formulas for the Dolbeault cohomology of Oeljeklaus-Toma manifolds admitting pluriclosed metrics.

KW - Bott-Chern cohomology

KW - Hermitian metric

KW - Oeljeklaus-Toma manifold

KW - SKT

KW - cohomology

KW - pluriclosed

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U2 - 10.5565/PUBLMAT6812409

DO - 10.5565/PUBLMAT6812409

M3 - Journal article

SN - 0214-1493

VL - 68

SP - 219

EP - 239

JO - Publicacions Matematiques

JF - Publicacions Matematiques

IS - 1

ER -

On metric and cohomological properties of Oeljeklaus-Toma manifolds

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Keywords

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