Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Hypersymplectic structures with torsion onLie algebroids
Publication Date:	2015-01-13
Authors:	- Paulo Antunes - Joana Margarida Nunes da Costa
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 hyperk¨ahler 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.
Institution:	DMUC 15-02
Online version:	http://www.mat.uc.pt...prints/eng_2015.html
Download:	Not available