A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space G3-Reference-Cited by-同舟云学术

A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space G3

Published:2023-07-03 Issue:13 Volume:11 Page:2971
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Al-Jedani Awatif¹^ORCID,Abdel-Baky Rashad A.²^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23890, Saudi Arabia

2. Department of Mathematics, Faculty of Science, University of Assiut, Assiut 71516, Egypt

Abstract

This article gives an approach for establishing a surface family with a mutual geodesic curve in Galilean 3-space G3. 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.

Funder

Deputyship for Research and Innovation, Ministry of Education in Saudi Arabia

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/13/2971/pdf

Reference20 articles.

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4. O’Neil, B. (1983). Semi-Riemannian Geometry Geometry, with Applications to Relativity, Academic Press.

5. Parametric representation of a surface pencil with a common spatial geodesic;Wang;Comput. Aided Des.,2004

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