Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space-Reference-Cited by-同舟云学术

Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space

Published:2024-06-12 Issue:6 Volume:16 Page:732
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Mofarreh Fatemah¹^ORCID

Affiliation:

1. Mathematical Science Department, Faculty of Sciences, Princess Nourah Bint Abdulrahman, Riyadh 11546, Saudi Arabia

Abstract

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (TLSC) with the symmetry of a Bertrand couple (BC) can be specified in terms of linear combinations of the components of the local frames in Minkowski 3-space E13. With these parametric representations, the necessary and sufficient conditions for the specified BC are derived to be the geodesic curves defining these surfaces. Afterward, the definition of a TL ruled surface (RS) is also provided. Furthermore, the application of the method to some significant models is given.

Funder

Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/6/732/pdf

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