2023/04/12 by Katarzyna Grabowska, Grabowska, Katarzyna, Janusz Grabowski +1
Mathematics · #37C10 #37C86 #53D10 #53D35 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2304.05891
openalex publication_date 2023/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A regular contact manifold is a manifold M equipped with a globally defined contact form η such that the topological space M/R of orbits (trajectories) of the Reeb vector field R of η carries a smooth manifold structure, so the canonical projection p:M→ M/R is a smooth fibration. We show that, under the additional assumption that R is a complete vector field, this fibration is actually either an S1- or an ℝ-principal bundle. Moreover, there exists a unique symplectic form ω on M/R such that p^*(ω)=dη which is ρ-integral in the S1-bundle case, where ρ is the minimal period of the S1-action, so the symplectic manifold (M/R,ω) admits a prequantization. We do not assume that M is compact.