Hyperstructures on Lie algebroids
Symplectic Geometry
2015-06-15 v1 Differential Geometry
Abstract
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, and structures.
Cite
@article{arxiv.1304.4102,
title = {Hyperstructures on Lie algebroids},
author = {P. Antunes and J. M. Nunes da Costa},
journal= {arXiv preprint arXiv:1304.4102},
year = {2015}
}