Hypersymplectic structures on Courant algebroids
Differential Geometry
2014-12-17 v1
Abstract
We introduce the notion of hypersymplectic structure on a Courant algebroid and we prove the existence of a one-to-one correspondence between hypersymplectic and hyperk\"ahler structures. This correspondence provides a simpler way to define a hyperk\"ahler structure on a Courant algebroid. We show that hypersymplectic structures on Courant algebroids encompass hyperk\"ahler and hyperk\"ahler structures with torsion on Lie algebroids. In the latter, the torsion existing at the Lie algebroid level is incorporated in the Courant structure. Cases of hypersymplectic structures on Courant algebroids which are doubles of Lie, quasi-Lie and proto-Lie bialgebroids are investigated.
Cite
@article{arxiv.1412.4992,
title = {Hypersymplectic structures on Courant algebroids},
author = {P. Antunes and J. M. Nunes da Costa},
journal= {arXiv preprint arXiv:1412.4992},
year = {2014}
}