Slant Helices that Constructed from Hyperspherical Curves in the n-dimensional Euclidean Space

Abstract

In this work, we study slant helices in the n-dimensional Euclidean space. We give methods to determine the position vectors of slant helices from arclength parameterized curves that lie on the unit hypersphere. By means of these methods, first we characterize slant helices and Salkowski curves which lie on 2n-dimensional hyperboloid. After that, we characterize rectifying slant helices which are geodesics of 2n-dimensional cone.