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

Awatif Al-Jedani and Rashad A. Abdel-Baky ()
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Awatif Al-Jedani: Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
Rashad A. Abdel-Baky: Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt

Mathematics, 2023, vol. 11, issue 19, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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