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

Authors : Bülent ALTUNKAYA

Pages : 229-240

Doi:10.36890/iejg.585408

View : 9 | Download : 10

Publication Date : 2019-10-03

Article Type : Research Paper

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.
Keywords : Slant helix, Salkowski curve, rectifying curve, hyperspherical curve, geodesic of a hypersurface