Hyperstructures on Lie algebroids

We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic structures and (pseudo-)hyperk\"{a}hler structures. We show that the hypersymplectic framework is very rich in already known compatible pairs of tensors such as Poisson-Nijenhuis, $\Omega N$ and $P \Omega$ structures.

Article: 
Hyperstructures on Lie algebroids
Authors: 
P. Antunes, J. M. Nunes da Costa
Journal: 
Arxiv
Year: 
2013
URL: 
http://arxiv.org/abs/1304.4102