Periodic orbits of analytic Euler fields on 3-manifolds

2019/11/05 by Francisco Torres de Lizaur, de Lizaur, Francisco Torres
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1911.01967

openalex publication_date 2019/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On any closed Riemannian 3-manifold which is not a torus bundle, every nonvanishing analytic solution of the stationary Euler equations has a periodic trajectory. This result is originally due to A. Rechtman (arXiv:0904.2719) and K. Cieliebak and E. Volkov (arXiv:1402.6484); here we present an alternative proof of it.

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