2023/09/26 by Malek Hanounah, Ines Kath, Hanounah, Malek +5 · 2 citations
Computer Science · Mathematics · #53B30 #53C50 #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2309.14955
openalex publication_date 2023/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave X by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a connected subgroup of the isometry group that acts properly cocompactly on X. We show that compact quotients of homogeneous plane waves are ``essentially" standard; more precisely, we show that they are standard or `semi-standard'. We find conditions which ensure that a quotient is not only semi-standard but even standard. As a consequence of these results, we obtain that the flow of the parallel isotropic vector field of a compact locally homogeneous plane wave is equicontinuous.