Slant helices in the Euclidean 3-space revisited

Abstract

In this paper, we study the surfaces whose geodesics are slant curves. We show that a unit speed curve $\gamma$ in the 3-dimensional Euclidean space is a slant helix if and only if it is a geodesic of a helix surface. We prove that the striction line of a helix surface is a general helix; as a consequence, slant helices are characterized as geodesics of the tangent surface of a general helix. Finally, we provide two methods for constructing slant helices in helix surfaces.