Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids

TL;DR

This paper introduces Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids, extending the concept of Koszul-Vinberg structures to a new symmetric setting related to Jacobi structures.

Contribution

It defines and explores properties of Jacobi-Koszul-Vinberg structures on Jacobi algebroids, a novel generalization in the field of algebroid geometry.

Findings

Properties of Jacobi-Koszul-Vinberg structures are established.

Definition of Jacobi-Koszul-Vinberg manifolds as symmetric analogues of Jacobi manifolds.

Extension of Koszul-Vinberg structures to Jacobi algebroids.

Abstract

A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to the structures on algebroids. A Koszul-Vinberg structure on a left-symmetric algebroid is regarded as a symmetric analogue of a Poisson structure on a Lie algebroid. We define a Jacobi-Koszul-Vinberg structure on a Jacobi-left-symmetric algebroid as a symmetric analogue of a Jacobi structure on a Jacobi algebroid. We show some properties of Jacobi-Koszul-Vinberg structures on Jacobi algebroids and give the definition of a Jacobi-Koszul-Vinberg manifold, which is a symmetric analogue of a Jacobi manifold.