Helical Transformations from Spherical to Rectifying Curves

Abstract

In this work, we characterize the relationships between spherical helices and rectifying helices in the Euclidean 3-space. By transforming a given spherical curve with specific geometric properties, we construct a corresponding rectifying helix. Our study establishes three key correspondences: first, spherical curves with constant curvature result in slant helices; second, spherical helices give rise to clad helices; and third, spherical slant helices lead to generalized clad helices. These findings contribute to a deeper understanding of the geometric interplay between different types of space curves.