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Contravariant Pseudo-Hessian manifolds and their associated Poisson structures
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: Submitted
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Symplectic Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2001.03776
- Document Type :
- Working Paper