On Darboux helices in Euclidean 4-space

Abstract

The notion of Darboux helix in Euclidean 3-space was introduced and studied by Yayli 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 kappa(2) + tau(2) = 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 V-4-slant helix are the same concepts.