Surfaces Using a Common Geodesic Curve With an Alternative Moving Frame in The 3- Dimensional Lie Group

Abstract

Our purpose in this research is to use an alternative moving frame in the 3-dimensional Lie group G to construct the problem of how to characterize a surface family and derive the conditions from a given common geodesic curve as an isoparametric curve. We also derive the relation about developability along the common geodesic of a ruled surface as a member of the surface family. Finally, we will give some examples to show some applications of the method.