Some characterizations for a quaternion-valued and dual variable curve (Q2003748)

Summary: Quaternions, which are found in many fields, have been studied for a long time. The interest in dual quaternions has also increased after real quaternions. Nagaraj and Bharathi developed the basic theories of these studies. The Serret-Frenet Formulae for dual quaternion-valued functions of one real variable are derived. In this paper, by making use of the results of some previous studies, helixes and harmonic curvature concepts in \(Q_{\mathbb{D}^3}\) and \(Q_{\mathbb{D}^4}\) are considered and a characterization for a dual harmonic curve to be a helix is given.