Surface Family with Bertrand Curves as Joint Asymptotic Curves in 3D Galilean Space

Abstract

The primary objective of this work is to discuss a surface family with the similarity of Bertrand curves in 3D Galilean space. Subsequently, by applying the Serret–Frenet frame, we estimate the sufficient and necessary statuses of a surface family with Bertrand curves as joint asymptotic curves. The dilation to ruled surfaces is also summarized. Meanwhile, the epitomes are illustrated to provide an explanation of the theoretical results.

Keywords

• isotropic normal
• Bertrand curves
• marching-scale functions