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.