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 E_1^3. 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.
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Öztürk et al. (2024) studied this question.
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