English

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, ΩN\Omega N and PΩP \Omega structures.

Keywords

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}
}
R2 v1 2026-06-21T23:59:42.861Z