Surface Family Pair with Bertrand Pair as Common Geodesic Curves in Galilean 3-Space 𝔾₃

Abstract

This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space G3. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile, some examples are provided to show the surfaces family with common Bertrand geodesic curves.

Keywords

• isotropic normal
• Serret–Frenet formulae
• Bertrand pair
• marching-scale functions