Darboux Associate Curves of Spacelike Curves in E₁³

In this paper, we introduce a new type of curve called the k-directional Darboux curve. These curves are generated by vector fields that are constructed using the Darboux frame of a given spacelike curve α lying on a timelike surface in Minkowski 3-space E₁³. We give the relationships between these curves and their curvatures. In particular, we show how k-directional Darboux curves can be used to classify some special curves, such as helices and slant helices.