Submanifolds in Koszul-Vinberg geometry

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 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 [\textit{Contravariant Pseudo-Hessian manifolds and their associated Poisson structures}. \rm{Differential 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.