2018/08/31 by Shintaro Akamine, Joseph Cho, Yuta Ogata
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Affine transformation #Classical mechanics #Conformal map #Differential geometry #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Invariant (physics) #Lorentz transformation #Mathematical analysis #Mathematical physics #Mathematics #Minimal surface #Parametrization (atmospheric modeling) #Physics #Pure mathematics #math.DG #msc:53A10 #msc:53A15 #msc:53B30 #msc:57R45
paper · pdf · doi:10.1007/s12220-019-00166-7
published as J. Geom. Anal. 30(1):731-761, 2020
arxiv created 2019/02/27 · openalex publication_date 2019/02/27 · openalex created_date 2019/03/02 · arxiv updated 2022/03/08 · openalex updated_date 2026/07/29
Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike minimal surfaces, to obtain a complete global classification of these surfaces and to characterize them using a geometric invariant called lightlike curvatures. As a result, we reveal the relationship between timelike Thomsen surfaces, and timelike minimal surfaces with planar curvature lines. As an application, we give a deformation of null curves preserving the pseudo-arclength parametrization and the constancy of the lightlike curvatures.