Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/44547
Title: | Hypersymplectic structures with torsion on Lie algebroids | Authors: | Antunes, Paulo Nunes da Costa, Joana Margarida |
Issue Date: | 2016 | Publisher: | Elsevier | Project: | info:eu-repo/grantAgreement/FCT/5876/147205/PT | Serial title, monograph or event: | Journal of Geometry and Physics | Volume: | 104 | Abstract: | Hypersymplectic structures with torsion on Lie algebroids are investigated. We show that each hypersymplectic structure with torsion on a Lie algebroid determines three Nijenhuis morphisms. From a contravariant point of view, these structures are twisted Poisson structures. We prove the existence of a one-to-one correspondence between hypersymplectic structures with torsion and hyperkähler structures with torsion. We show that given a Lie algebroid with a hypersymplectic structure with torsion, the deformation of the Lie algebroid structure by any of the transition morphisms does not affect the hypersymplectic structure with torsion. We also show that if a triplet of 2-forms is a hypersymplectic structure with torsion on a Lie algebroid A, then the triplet of the inverse bivectors is a hypersymplectic structure with torsion for a certain Lie algebroid structure on the dual A*, and conversely. Examples of hypersymplectic structures with torsion are included. | URI: | https://hdl.handle.net/10316/44547 | DOI: | 10.1016/j.geomphys.2016.01.010 10.1016/j.geomphys.2016.01.010 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Antunes_NunesdaCosta_JGP_2016.pdf | 438.08 kB | Adobe PDF | View/Open |
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