New characterizations of spacelike curves on timelike surfaces through the link of specific frames

Abstract

In this work, considering a regular spacelike curve on a smooth timelike surface in Minkowski 3-space, we investigate relations between the mentioned curve’s Darboux and Bishop frames on the timelike surface. Next we obtain Darboux vector of the regular spacelike curve in terms of Bishop apparatus. Thereafter, translating the Darboux vector to the center of the unit sphere, we determine aforementioned spacelike curve. Moreover, we investigate this spherical image’s Frenet-Serret and Bishop apparatus and illustrate our results with two examples.