Contravariant Pseudo-Hessian manifolds and their associated Poisson structures

Autor:	Abouqateb, Abdelhak, Boucetta, Mohamed, Bourzik, Charif
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematics - Symplectic Geometry
Druh dokumentu:	Working Paper
Popis:	A contravariant pseudo-Hessian 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 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 $(M,\nabla,h)$ 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. Comment: Submitted
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.03776 Zobrazit plný text záznamu View this record from Arxiv