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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 1 (January 2025)   > Article

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

Compatibilité d’une structure de Jacobi et une structure Riemannienne sur une algébroïde de Lie


Yacine Aït Amrane
USTHB
Algeria

Ahmed Zeglaoui
Université de Saida Dr Moulay Tahar
Algeria



Published on 20 January 2025   DOI : 10.21494/ISTE.OP.2025.1254

Abstract

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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.

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.

Jacobi structure Riemannian Poisson structure Kenmotsu structure Locally conformally Kähler structure Lie algebroid

Jacobi structure Riemannian Poisson structure Kenmotsu structure Locally conformally Kähler structure Lie algebroid

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