Special Helices on the Ellipsoid

Abstract

In this study, we investigate three types of special helices whose axis is a fixed constant Killing vector field on the Ellipsoid $% \mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ in $\mathbb{R}_{a_{1},a_{2},a_{3}}^{3}$. Then, we obtain the curvatures of all special helices on the ellipsoid $% \mathbb{S}_{a_{1},a_{2},a_{3}}^{2}$ and give some characterizations of these curves. Moreover, we present various examples and visualize their images using the Mathematica program.