Dirac pairs

Details Dirac pairs Dirac pairs

2011-04-07

arxiv.org/abs/1104.1378v1

Mathematics

Differential Geometry

dedicated to Tudor Ratiu, 23 pages

Scientific paper

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.

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