On some new frames along a space curve and integral curves with Darboux q-vector fields in E 3

Abstract

In this paper, to start we defined osculating q -frame, normal q -frame, and rectifying qframe along a space curve in Euclidean 3 -space 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 d o -direction curve, d n -direction curve and d r -direction curve. Finally, we gave some theorems and results related with these curves.