Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space-Reference-Cited by-同舟云学术

Surface Pencil Couple with Bertrand Couple as Joint Principal Curves in Galilean 3-Space

Published:2023-10-30 Issue:11 Volume:12 Page:1022
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Alluhaibi Nadia¹^ORCID,Abdel-Baky Rashad A.²

Affiliation:

1. Department of Mathematics, Science and Arts College, King Abdulaziz University, Rabigh 21911, Saudi Arabia

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

Abstract

A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret–Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/11/1022/pdf

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