Conformally symplectic structures and the Lefschetz condition

This short note provides a symplectic analogue of Vaisman’s theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mut...

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Main Authors: Lejmi, Mehdi, Wilson, Scott O.
Format: Article
Language:English
Published: Académie des sciences 2024-11-01
Series:Comptes Rendus. Mathématique
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Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.660/
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author Lejmi, Mehdi
Wilson, Scott O.
author_facet Lejmi, Mehdi
Wilson, Scott O.
author_sort Lejmi, Mehdi
collection DOAJ
description This short note provides a symplectic analogue of Vaisman’s theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mutually compatible almost complex structure.
format Article
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institution Kabale University
issn 1778-3569
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publishDate 2024-11-01
publisher Académie des sciences
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series Comptes Rendus. Mathématique
spelling doaj-art-bec9de0965b04e04ac2aa83d535b2a152025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111491149510.5802/crmath.66010.5802/crmath.660Conformally symplectic structures and the Lefschetz conditionLejmi, Mehdi0https://orcid.org/0000-0002-7489-9149Wilson, Scott O.1https://orcid.org/0000-0002-2463-6148Department of Mathematics, Bronx Community College, City University of New York, 2155 University Av., Bronx, NY 10453, USA.Department of Mathematics, Queens College, City University of New York, 65-30 Kissena Blvd., Flushing, NY 11367, USA.This short note provides a symplectic analogue of Vaisman’s theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in fact globally conformally symplectic, whenever there is a mutually compatible almost complex structure.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.660/Locally conformally symplectic structureshard Lefschetz conditionalmost complex structures
spellingShingle Lejmi, Mehdi
Wilson, Scott O.
Conformally symplectic structures and the Lefschetz condition
Comptes Rendus. Mathématique
Locally conformally symplectic structures
hard Lefschetz condition
almost complex structures
title Conformally symplectic structures and the Lefschetz condition
title_full Conformally symplectic structures and the Lefschetz condition
title_fullStr Conformally symplectic structures and the Lefschetz condition
title_full_unstemmed Conformally symplectic structures and the Lefschetz condition
title_short Conformally symplectic structures and the Lefschetz condition
title_sort conformally symplectic structures and the lefschetz condition
topic Locally conformally symplectic structures
hard Lefschetz condition
almost complex structures
url https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.660/
work_keys_str_mv AT lejmimehdi conformallysymplecticstructuresandthelefschetzcondition
AT wilsonscotto conformallysymplecticstructuresandthelefschetzcondition