Constant Ratio Quaternionic Curves in Euclidean Spaces

Abstract

In this paper, we give some characterizations of quaternionic curves whose position vectors can be written as linear combinations of their Serret-Frenet vectors in Euclidean 3-space \({\mathbb{E}^{3}}\) and Euclidean 4-space \({\mathbb{E}^{4}}\). We characterize such curves in terms of their curvature functions. Finally, we give the necessary and sufficient conditions for these types of curves to become constant ratio, T-constant, and N-constant.