A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">G</mi><mn>3</mn></msub></semantics></math></inline-formula>

Abstract

This article gives an approach for establishing a surface family with a mutual geodesic curve in Galilean 3-space G3. Given a smooth space curve, we derive the sufficient and necessary condition for the given curve to be geodesic on it. Furthermore, we resolve the conditions when the surface is a ruled surface. Consequently, its ability to develop with the mutual geodesic of the elements of the surface family is researched. Meanwhile, we explain this approach by submitting considerable examples.

Keywords

• isotropic normal
• geodesic curve
• ruled and developable surfaces
• Serret–Frenet formulae
• marching-scale functions