2024/01/17 by Victoria Bencheva, Bencheva, Victoria, Velichka Milousheva +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #53A35 #53B25 #53B30 #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2401.09024
openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge problem for this class of surfaces.