2022/08/28 by Asuka Hagiwara, Hagiwara, Asuka
Mathematics · #37C85 #37C86 (Primary) #53D10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2208.13148
openalex publication_date 2022/08/28 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2n on a (2n + r)-dimensional closed manifold M. For r = 2, we prove that the foliation has at least two leaves which are homeomorphic to a 2-dimensional torus, if M admits a locally free T2-action which preserves dα and satisfies that the function α(Z2) is constant, where Z1, Z2 are the infinitesimal generators of the T2-action. We also give its generalization for r ≥ 1.