2023/09/09 by Naoki Kimura, Kimura, Naoki, Tomoya Nakamura +1
Mathematics · Medicine · #53D10 #53D15 #53D17 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2309.04775
openalex publication_date 2023/09/09 · openalex created_date 2023/09/14 · openalex updated_date 2026/07/28
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.