Work

On the geometry of compatible Poisson and Riemannian structures

Year: 2025

Type: article

Abstract: We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant Levi-Civita connection. These include Riemann–Poisson structures (as defined by M. Boucetta), and the class of almost Kähler–Poisson manifolds, introduced with the aid of a contravariant f -structure, that will be called partially co-complex structure , in analogy with complex ones on Kähler manifolds. Additionally, we study the geometry of the symplectic foliation, and the behavior of these compatibilities under structure preserving maps and symmetries.

Source: Journal of Geometry and Physics

DOI: 10.1016/j.geomphys.2025.105593

Authors: Nicolás Martínez Alba, Andrés Vargas

Institutions: Universidad Nacional de Colombia, Pontificia Universidad Javeriana

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Pontificia Universidad Javeriana