A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space G 3

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 13, 1-12

Abstract: This article gives an approach for establishing a surface family with a mutual geodesic curve in Galilean 3-space G 3 . 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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