Submanifolds in Koszul-Vinberg geometry

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 pseu...

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Veröffentlicht in:arXiv.org 2021-04
Hauptverfasser: Abouqateb, Abdelhak, Boucetta, Mohamed, Bourzik, Charif
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description 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.
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title Submanifolds in Koszul-Vinberg geometry
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