Double bracket structures on Poisson manifolds
Differential Geometry
2014-02-18 v1
Abstract
On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of the normal metric such that the above vector field restricted to the symplectic leaf is a gradient vector field with respect to this metric.
Cite
@article{arxiv.1402.3958,
title = {Double bracket structures on Poisson manifolds},
author = {Petre Birtea},
journal= {arXiv preprint arXiv:1402.3958},
year = {2014}
}