Charif Bourzik

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20202025

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math.DG2025

Invariant Poisson Structures on Homogeneous Manifolds: Algebraic Characterization, Symplectic Foliation, and Contravariant Connections

Abdelhak Abouqateb, Charif Bourzik

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in th…

math.DG2021

Submanifolds in Koszul-Vinberg geometry

Abdelhak Abouqateb, Mohamed Boucetta, Charif Bourzik

A Koszul-Vinberg manifold is a manifold $M$ endowed with a pair $(\nabla, h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a generalized Coda…

math.DG2020

Contravariant Pseudo-Hessian manifolds and their associated Poisson structures

Abdelhak Abouqateb, Mohamed Boucetta, Charif Bourzik

A contravariant pseudo-Hessian manifold is a manifold $M$ endowed with a pair $(\nabla, h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a co…