Compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids
Symplectic Geometry
2023-09-12 v1 Differential Geometry
Abstract
We define compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids. This notion is a generalization of the compatibility between Poisson structures and pseudo-Riemannian cometrics on manifolds, which was defined by Boucetta. We show that the compatibility with a cometric is ``preserved'' by the Poissonization of a Jacobi structure. Furthermore, we prove that for a contact pseudo-metric structure on a manifold, satisfying the compatibility condition is equivalent to being a Sasakian pseudo-metric structure.
Keywords
Cite
@article{arxiv.2309.04775,
title = {Compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids},
author = {Naoki Kimura and Tomoya Nakamura},
journal= {arXiv preprint arXiv:2309.04775},
year = {2023}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:2112.03495