Translation surfaces according to Frenet frame in Minkowski 3-space

摘要

In this paper, using non-planar space curves, the translation surfaces were investigated according to Frenet frames in Minkowski 3-space and some properties of these surfaces were given. Furthermore, we calculated first fundamental form, second fundamental form, Gaussian curvature and mean curvature of the translation surface. Also, the Darboux frame of the generator curves of the translation surfaces in Minkowski 3-space was given. Finally, we gave the conditions of being a geodesic, an asymptotic line and a principal line for the generator curves of the translation surface.