arXiv subjects

Yacine Aït Amrane

Publications and source records attributed to Yacine Aït Amrane.

4 recordsLinked to original sources

arXiv2019

Compatibility of a Jacobi structure and a Riemannian structure on a Lie algebroid

In a preceding paper we introduced a notion of compatibility between a Jacobi structure and a Riemannian structure on a smooth manifold. We proved that in the case of fundamental examples of Jacobi structures : Poisson structures, contact structures and locally conformally symplectic structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, (1/2)-Kenmotsu structures and locally conformally Kähler structures. In this paper we are generalizing this work to the framework of Lie algebroids.

math.DG↗

arXiv2017

Compatibilité des structures riemanniennes et des structures de Jacobi

We give a notion of compatibility between a Riemannian metric and a Jacobi structure. We prove that in case of Poisson structures, contact structures and locally conformally symplectic structures, fundamental examples of Jacobi structures, we get respectively Riemann-Poisson structures in the sense of M. Boucetta, $\frac{1}{ 2}$-Kenmotsu structures and locally conformally Kähler structures.

math.DG↗

arXiv2015

Warped Poisson Brackets on Warped Products

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these bivector fields will be called the warped bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.

math.DG↗

arXiv2010

Automorphic representations and harmonic cochains for $GL_{n+1}$

Let $K$ be a global field of positive characteristic. Let $\infty$ be a fixed place of $K$. This paper gives an explicit isomorphism between the space of automorphic forms (resp. cusp forms) for $GL_{n+1}(K)$ that transform like the special representations and certain spaces of harmonic cochains (resp. those with finite support) defined on the Bruhat-Tits building of $GL_{n+1}(K_\infty)$.

math.RT↗