Turkish Journal of Mathematics
Abstract
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.
DOI
10.55730/1300-0098.3509
Keywords
canonical parameters, fundamental theorem, Parallel normalized mean curvature vector field
First Page
327
Last Page
345
Recommended Citation
BENCHEVA, V, & MILOUSHEVA, V (2024). Timelike surfaces with parallel normalized mean curvature vector field in the Minkowski 4-space. Turkish Journal of Mathematics 48 (2): 327-345. https://doi.org/10.55730/1300-0098.3509
