Double bracket structures on Poisson manifolds

Petre Birtea

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arXiv · 1402.3958

Double bracket structures on Poisson manifolds

Petre Birtea

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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.

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BibTeX RIS

Petre Birtea. 2014-02-17. Double bracket structures on Poisson manifolds. https://arxiv.org/abs/1402.3958

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