Curl vector fields and quadratic Poisson structures. (Rotationnels et structures de Poisson quadratiques.) (French) Zbl 0719.58001

Dufour, Jean-Paul; Haraki, Abdeljalil

C. R. Acad. Sci., Paris, Sér. I 312, No. 1, 137-140 (1991).

It is given a characterization of the quadratic Poisson structures whose eigenvalues verify some generic condition. A complete classification of the 3-dimensional quadratic Poisson structures is also stated.

Reviewer: D.Motreanu (Iaşi)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D17	Poisson manifolds; Poisson groupoids and algebroids
58A30	Vector distributions (subbundles of the tangent bundles)
17B63	Poisson algebras

Keywords:

Poisson structure; curl vector field; tensors; eigenvalues; local coordinates