A. Abouqateb

activity

20022026

most citedSpecial Affine Connections on Symmetric Spaces

1 citations · 1 across the 6 of their papers we have counts for

collaborators

8 papers

math.DG2026

A complete description of solvable symplectic Lie algebras

Abdelhak Abouqateb, Saïd Benayadi, Othmane Dani

In this paper, we present a complete characterization of solvable symplectic Lie algebras via a symplectic double extension process. We demonstrate that any such algebra is either…

math.DG2025

Some invariant connections on symplectic reductive homogeneous spaces

Abdelhak Abouqateb, Othmane Dani

A symplectic reductive homogeneous space is a pair $(G / H, Ω)$ , where $G / H$ is a reductive homogeneous $G$ -space and $Ω$ is a $G$ -invariant symplectic form on it. The main examples i…

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.DG2023★ 1 cited

Special Affine Connections on Symmetric Spaces

Othmane Dani, Abdelhak Abouqateb

Let $(G, H, σ)$ be a symmetric pair and $g = m \oplus h$ the canonical decomposition of the Lie algebra $g$ of $G$ . We denote by $\nabla^{0}$ …

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…