Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3509
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.
Keywords
canonical parameters, fundamental theorem, Parallel normalized mean curvature vector field
First Page
327
Last Page
345
Recommended Citation
BENCHEVA, VICTORIA and MILOUSHEVA, VELICHKA
(2024)
"Timelike surfaces with parallel normalized mean curvature vector field in the
Minkowski 4-space,"
Turkish Journal of Mathematics: Vol. 48:
No.
2, Article 15.
https://doi.org/10.55730/1300-0098.3509
Available at:
https://journals.tubitak.gov.tr/math/vol48/iss2/15
