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arXiv · 2309.04775

Compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids

Naoki Kimura·Tomoya Nakamura
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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.

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Naoki Kimura, Tomoya Nakamura. 2023-09-09. Compatibility between Jacobi structures and pseudo-Riemannian cometrics on Jacobi algebroids. https://arxiv.org/abs/2309.04775

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