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.
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Öztürk, G., Kişi, İ. & Büyükkütük, S. Constant Ratio Quaternionic Curves in Euclidean Spaces. Adv. Appl. Clifford Algebras 27, 1659–1673 (2017). https://doi.org/10.1007/s00006-016-0716-4
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DOI: https://doi.org/10.1007/s00006-016-0716-4