Hyperstructures on Lie algebroids (Q2871272)

The present paper deals with hypersymplectic structures on Lie algebroids generalizing the hypersymplectic structures on manifolds. As usual, all classical results and examples of hypersymplectic structures on manifolds hold in the Lie algebroids framework. A 1--1 correspondence is proved between hypersymplectic and hyper-Kähler structures on a Lie algebroid. Also, the authors prove that hypersymplectic structures on a Lie algebroid provide other types of interesting structures on the Lie algebroid, such as Poisson-Nijenhuis structures.