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