A-Poisson structures

Details A-Poisson structures A-Poisson structures

2010-10-17

arxiv.org/abs/1010.3398v1

Int. J. Contemp. Math. Sciences, vol .7, 2012, no.16, 785-803

Mathematics

Differential Geometry

17 pages

Scientific paper

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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