Please use this identifier to cite or link to this item: http://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: http://hdl.handle.net/10316/44547
Other Identifiers: 10.1016/j.geomphys.2016.01.010
DOI: 10.1016/j.geomphys.2016.01.010
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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