2021/04/18 by Abdelhak Abouqateb, Abouqateb, Abdelhak, Mohamed Boucetta +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.2104.08748
27 pages
arxiv created 2021/04/18 · arxiv updated 2021/04/20
A Koszul-Vinberg manifold is a manifold M endowed with a pair (∇,h) where ∇ is a flat connection and h is a symmetric bivector field satisfying a generalized Codazzi equation. The geometry of such manifolds could be seen as a type of bridge between Poisson geometry and pseudo-Riemannian geometry, as has been highlighted in our previous article [Contravariant Pseudo-Hessian manifolds and their associated Poisson structures. \rmDifferential Geometry and its Applications (2020)]. Our objective here will be to pursue our study by focusing in this setting on submanifolds by taking into account some developments in the theory of Poisson submanifolds.