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

Abstract

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.

Keywords

• q-frame
• integral curve
• osculating q-frame
• normal q-frame
• rectifying q-frame