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 D 3 and Q D 4 are considered and a characterization for a dual harmonic curve to be a helix is given.

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ÖZ On a Study of the Quaternionic Lorentzian Curve ABSTRACTIn this study, Serret-Frenet Formulas for a space-quaternionic curve were obtained by considering quaternions and pseudoquaternions in three-dimensional Lorentz Space L Q 3 . The Serret-Frenet Formulas for a Quaternionic Lorentz Curve L Q 4 were then re-derived using them.

This paper studies the CR-submanifolds of a Kaehlerian manifold which have holomorphic vector fîelds on them. İt is shown that a CR-submanifold having holomorphic vector fîelds on it is a CR-product.

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Abstract:In this paper, we study the position vectors of a timelike curve in the Minkowski 3-space R 3 1 . We give some characterizations for timelike curves which lie on some subspaces of R 3 1 .