On Darboux helices in Euclidean 4‐space

Abstract

The notion of Darboux helix in Euclidean 3‐space was introduced and studied by Yaylı et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality κ2 + τ2 = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4‐space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V4‐slant helix are the same concepts.