On the quaternionic curves according to parallel transport frame

Abstract

In this paper, we have studied parallel transport frame for a quaternionic curve in E3 and E4. Firstly, we have defined a new kind of slant helix with respect to parallel transport frame and given some necessary and sufficient conditions for the quaternionic slant helix in E3. We have introduced a new definition of harmonic curvature functions in terms of M3 according to parallel transport frame and defined quaternionic M3−slant helix by using the new harmonic curvature functions in E4.