Rotation minimizing frames and quaternionic rectifying curves (original) (raw)

In this paper, certain characterizations of a Rotation minimizing frame (RMF) are studied. An RMF is obtained on the direction curve ∫ N(s)ds using a unit quaternionic curve. Some properties of this frame are given. Also, the condition of being a quaternionic rectifying curve and the condition of being a spherical curve is expressed using this frame. Moreover, the characterization of quaternionic rectifying curves is obtained similar to the characterization of spherical curves. Finally, the properties of the quaternionic rectifying curves are given.