• 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. 
View PDF on arXiv
122 Citations
Highly Influential Citations
4
Background Citations
45
Methods Citations
11
Results Citations
2

122 Citations

Prolongation of Poisson 2-form on Weil bundles

In this paper, M denotes a smooth manifold of dimension n, A a Weil algebra and M^{A} the associated Weil bundle. When (M,_{M}) is a Poisson manifold with 2-form _{M}, we construct the 2-Poisson form…

A Laplace operator for Poisson manifolds

Symplectic structures on stratified pseudomanifolds

. We introduce a sheaf-theoretic definition of symplectic form on a smooth stratified pseudomanifold in the framework of C ∞ -ringed space theory. This structure gives an isomorphism between the…

A Poisson bracket on the space of Poisson structures

Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form.…

Poisson structures of near-symplectic manifolds and their cohomology

We connect Poisson and near-symplectic geometry by showing that there is an almost regular Poisson structure induced by a near-symplectic form $\omega$ when its singular locus is a symplectic mapping…

On the symplectic realization of Poisson-Nijenhuis manifolds

We consider the problem of the symplectic realization of a Poisson-Nijenhuis manifold. By applying a new technique developed by M. Crainic and I. Myarcut¸ for the study of the above problem in the…

Regular Foliations and Poisson Structures on Orientable Manifolds

On an orientable manifold M, we consider a regular even dimensional foliation F which is globally defined by a set of k-independent 1-forms. We give necessary and sufficient conditions for the…

Structures de Jacobi sur une variété des points proches

We consider a local algebra A (in the sense of Andr\'e Weil), M a smooth paracompact manifold and M^{A} the manifold of infinietly near points on M of kind A. In this paper, we define and study the…

Double bracket structures on Poisson manifolds

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…

Poisson Structures on Trivial Extension Algebras

. We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one–to–one correspondence…
...

References

SHOWING 1-6 OF 6 REFERENCES

Champs de vecteurs et formes différentielles sur une variété des points proches

Let M be a smooth manifold, A a local algebra in sense of Andre Weil, M A the manifold of near points on M of kind A and X(M A ) the module of vector fields on M A. We give a new definition of vector…

Lectures on the geometry of Poisson manifolds

0 Introduction.- 1 The Poisson bivector and the Schouten-Nijenhuis bracket.- 1.1 The Poisson bivector.- 1.2 The Schouten-Nijenhuis bracket.- 1.3 Coordinate expressions.- 1.4 The Koszul formula and…

Relèvements des structures symplectiques et pseudo-riemanniennes à des variétés de points proches

On considère une variété différentielle M, paracompacte de classe C∞. Etant donné une algèbre locale A (algèbre commutative unitaire de dimension finie sur R dont l’idéal maximal m est de codimension…

Prolongement des champs de vecteurs à des variétés de points proches

Etant donnee une variete differentielle paracompacte M de classe C ∞ et une algebre locale A de dimension finie sur R ayant un ideal maximal de codimension 1, on note M A la variete des points…

Théorie des points proches sur les variétés différentiables

Prolongation of connections to bundles of infinitely near points

The purpose of this paper is to generalize the results of [5] to the bundles of infinitely near points of A -kinds in the sense of A. Weil [7], which generalizes the notions of p-jets in the sense of…