Open Access

ARTICLE

Frenet Curve Couples in Three Dimensional Lie Groups

Osman Zeki Okuyucu^*
Department of Mathematics, Faculty of Science and Arts, Bilecik ¸Seyh Edebali University, Bilecik, Turkey
* Corresponding Author: Osman Zeki Okuyucu. Email:
(This article belongs to this Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 133(3), 653-671. https://doi.org/10.32604/cmes.2022.021081

Received 26 December 2021; Accepted 28 March 2022; Issue published 03 August 2022

Abstract

In this study, we examine the possible relations between the Frenet planes of any given two curves in three dimensional Lie groups with left invariant metrics. We explain these possible relations in nine cases and then introduce the conditions that must be met to coincide with the planes of these curves in nine theorems.

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Keywords

Curves; lie groups; curvatures; Frenet plane

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