A New Method to Obtain PH-Helical Curves in En+1

Abstract

Helical curves are constructed by the property that their unit tangents make a constant angle with a chosen constant direction. There are relations between polynomial planar curves, helices and Pythagorean-hodograph or shortly PH-curves. The aim of this paper is to obtain a method which generate PH-curves and PH-helical curves from a planar curve in Euclidean Space En+1. Furthermore, some examples are given in E4 and E5 to explain the method neatly.