2020/01/11 by Abdelhak Abouqateb, Abouqateb, Abdelhak, Mohamed Boucetta +3
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.2001.03776
Submitted
arxiv created 2020/01/11 · openalex publication_date 2020/01/11 · arxiv updated 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A contravariant pseudo-Hessian manifold is a manifold M endowed with a pair (∇,h) where ∇ is a flat connection and h is a symmetric bivector field satisfying a contravariant Codazzi equation. When h is invertible we recover the known notion of pseudo-Hessian manifold. Contravariant pseudo-Hessian manifolds have properties similar to Poisson manifolds and, in fact, to any contravariant pseudo-Hessian manifold (M,∇,h) we associate naturally a Poisson tensor on TM. We investigate these properties and we study in details many classes of such structures in order to highlight the richness of the geometry of these manifolds.