• Corpus ID: 119009288

A-Poisson structures

@article{Bossoto2010APoissonS,
  title={A-Poisson structures},
  author={Basile Guy Richard Bossoto and Eug{\`e}ne Okassa},
  journal={arXiv: Differential Geometry},
  year={2010}
}
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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