On generalized Darboux frame of a spacelike curve lying on a lightlike surface in Minkowski space $\mathbb{E}^{3}_{1}$

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that has two such frames and obtain frame's equations. find the relations between curvature functions $k_g$, $k_n$, $\tau_g$ with respect to its $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ frames. show exist along straight line ruled which is not entirely lightlike, but contains some points. define surfaces tangent binormal indicatrix null Cartan are principal lines having $\tilde{\tau}_{g}=0$ give examples.