Dirac pairs
Differential Geometry
2012-12-05 v1 Mathematical Physics
math.MP
Abstract
We extend the definition of the Nijenhuis torsion of an endomorphism of a Lie algebroid to that of a relation, and we prove that the torsion of the relation defined by a bi-Hamiltonian structure vanishes. Following Gelfand and Dorfman, we then define Dirac pairs, and we analyze the relationship of this general notion with the various kinds of compatible structures on manifolds, more generally on Lie algebroids.
Cite
@article{arxiv.1104.1378,
title = {Dirac pairs},
author = {Yvette Kosmann-Schwarzbach},
journal= {arXiv preprint arXiv:1104.1378},
year = {2012}
}
Comments
dedicated to Tudor Ratiu, 23 pages