Associated curves of a Frenet curve in the dual Lorentzian space

In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectively. explain with an example for second case. Finally, according to causal character rectifying $\mathbb{D}_{1}^{3}$, correspond any timelike spacelike ruled surface Minkowski 3−space R R13