6 citations · 8 across the 5 of their papers we have counts for
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Poisson structures compatible with the canonical metric on $\reel^3$
Mohamed Boucetta
In this Note, we will characterize the Poisson structures compatible with the canonical metric of $\reel^3$. We will also give some relvant examples of such structures. The notion…
On the Riemann-Lie algebras and Riemann-Poisson Lie groups
Mohamed Boucetta
A Riemann-Lie algebra is a Lie algebra such that its dual carries a Riemannian metric compatible (in the sense introduced by th author in C. R. Acad. Paris, t…
The modular class of a regular Poisson manifold and the Reeb invariant of its symplectic foliation
A. Abouqateb, M. Boucetta
We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps…
Riemann Poisson manifolds and Kähler-Riemann foliations
Mohamed Boucetta
Riemann Poisson manifolds were introduced by the author in [1] and studied in more details in [2]. Kähler-Riemann foliations form an interesting subset of the Riemannian foliations…
Poisson manifolds with compatible pseudo-metric and pseudo-Riemannian Lie algebras
Mohamed Boucetta
The notion of Poisson manifold with compatible pseudo-metric was introduced by the author in [1]. In this paper, we introduce a new class of Lie algebras which we call a pseudo-Rie…
Compatibility betwenn pseudo-riemannian structure and Poisson structure
Mohamed Boucetta
We will introduce two notions of compatibility bettwen pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced by Fernandes R. L., we…