A-Poisson structures

2010/10/17 by Basile Guy Richard Bossoto, Eugène Okassa · 2 citations
Mathematics · #math.DG #msc:17D63 #msc:53D17 #msc:53D05 #msc:58A32

paper · pdf

published as Int. J. Contemp. Math. Sciences, vol .7, 2012, no.16, 785-803 · 17 pages

arxiv created 2010/10/17 · arxiv updated 2012/04/17

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.

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