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arXiv · 2412.20103

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

Naoki Kimura·Tomoya Nakamura
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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.

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Naoki Kimura, Tomoya Nakamura. 2024-12-28. Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids. https://arxiv.org/abs/2412.20103

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