Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256078 | Journal of Geometry and Physics | 2016 | 15 Pages |
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 Aâ, and conversely. Examples of hypersymplectic structures with torsion are included.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
P. Antunes, J.M. Nunes da Costa,