English

A-Poisson structures

Differential Geometry 2012-04-17 v1

Abstract

Let M be a paracompact differentiable manifold, A a local algebra and M^{A} a manifold of infinitely near points on M of kind A. We define the notion of A-Poisson manifold on M^{A}. We show that when M is a Poisson manifold, then M^{A} is an A-Poisson manifold. We also show that if (M,) is a symplectic manifold, the structure of A-Poisson manifold on M^{A} defined by ^{A} coincide with the prolongation on M^{A} of the Poisson structure on M defined by the symplectic form.

Keywords

Cite

@article{arxiv.1010.3398,
  title  = {A-Poisson structures},
  author = {Basile Guy Richard Bossoto and Eugène Okassa},
  journal= {arXiv preprint arXiv:1010.3398},
  year   = {2012}
}

Comments

17 pages

R2 v1 2026-06-21T16:29:35.395Z