On some new frames along a space curve and integral curves with Darboux q-vector fields in ${\mathbb{E}}^3$

In this paper, to start we defined osculating q-frame, normal q-frame, and rectifying q-frame along a space curve in Euclidean 3-space ${\mathbb{E}}^3$ by using the Darboux vector field of the q-frame. We obtained the derivative equations of these new frames. Later, we defined some new integral curves of a space curve and called them ${\overline{\mathsf{d}}}_o$-direction curve, ${\overline{\mathsf{d}}}_n$-direction curve and ${\overline{\mathsf{d}}}_r$-direction curve. Finally, we gave some theorems and results related with these curves.