Helical Transformations from Spherical to Rectifying Curves

Year 2025, Volume: 13 Issue: 2, 292 - 299, 31.10.2025

Bülent Altunkaya

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.

Keywords

Rectifying helix , spherical curve , Sabban frame , helix , slant helix , clad helix , g-clad helix.

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