New characterization of vector field on Weil bundles
Let M be a paracompact smooth manifold, A a Weil algebra and M^A the associated Weil bundle. In this paper, we give another definition and characterization of vector field on M^A.
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arXiv subjects
Eugène Okassa
Publications and source records attributed to Eugène Okassa.
Parallelism between locally conformal symplectic manifolds and contact manifolds
We give the parallelism between locally conformal symplectic manifolds and contact manifolds. We also give the generalization of exact contact manifolds.
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Lie algebra of an n-Lie algebra
We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.
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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 André 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 fields on M^{A} and we show that X(M^{A}) is a Lie algebra over A. We study the cohomology of A-differential forms.
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A-Poisson structures
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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