Abstract
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 [Contravariant Pseudo-Hessian manifolds and their associated Poisson structures. 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.
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Abouqateb, A., Boucetta, M. & Bourzik, C. Submanifolds in Koszul–Vinberg Geometry. Results Math 77, 19 (2022). https://doi.org/10.1007/s00025-021-01557-5
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DOI: https://doi.org/10.1007/s00025-021-01557-5