On the Construction of a Surface Family with Common Geodesic in Galilean Space G3

Abstract

In this paper, we investigate the parametric representation for a family of surfaces through a given geodesic curve G3. We provide necessary and sufficient conditions for this curve to be an isogeodesic curve on the parametric surfaces using Frenet frame in Galilean space. Also, for the sake of visualizing of this study, we plot an example for this surfaces family.

Keywords

• geodesic curve
• isoparametric curve
• parametric surface
• galilean space
• 02.40.-k