Soyfidan, T.; Parlatici, H.; Güngör, M. A.

In this paper, we have studied parallel transport frame for a quaternionic curve in E-3 and E-4. 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 E-3. We have introduced a new definition of harmonic curvature functions in terms of M-3 according to parallel transport frame and defined quaternionic M-3-slant helix by using the new harmonic curvature functions in E-4.