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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Awatif Al-Jedani & Rashad A. Abdel-Baky, 2023. "A Surface Family with a Mutual Geodesic Curve in Galilean 3-Space G 3," Mathematics, MDPI, vol. 11(13), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2971-:d:1186052
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