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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Académie des sciences
2024-11-01
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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 |
id | doaj-art-bec9de0965b04e04ac2aa83d535b2a15 |
institution | Kabale University |
issn | 1778-3569 |
language | English |
publishDate | 2024-11-01 |
publisher | Académie des sciences |
record_format | Article |
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 |