Quaternionic Curves Which Lie on the Special Planes in 4−Dimensional Euclidean Space E4

Abstract

In this study, some curvature conditions of quaternionic curves are obtained by writing the position vectors of quaternionic curves as linear combinations of new vector fields, named as Di (1 ≤ i ≤ 4), that are produced from Frenet frame fields of the quaternionic curves. Also, the relations between DiDj‐quaternionic curves and the rectifying quaternionic curves and the osculating quaternionic curves are presented. Moreover, the results obtained are illustrated with an example in which the new vector fields are examined.