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Research Article | Open Access

A novel method for Mannheim curves in the Galilean 3−space G3

Mervat Elzawy1,2( ), Safaa Mosa3,4
Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
Mathematics Department, College of Science, Taibah University, Medina, Kingdom of Saudi Arabia
Mathematics Department, College of Science, University of Bisha, Bisha, Saudi Arabia
Mathematics Department, Faculty of Science, Damanhour University, Damanhour, Egypt
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Abstract

This research presents a novel method for Mannheim curves in three-dimensional Galilean space G3. Using this method, the necessary and sufficient conditions, along with the established results, must be satisfied for a curve in G3 to qualify as a Mannheim curve. Furthermore, relevant examples and graphs are provided to demonstrate how Mannheim curves and their partners can correspond to Salkowski and anti-Salkowski curves. Finally, in G3, the Mannheim partner curves are described.

Keywords

Mannheim curvesslant helicesSalkowski curvesCurves of Anti-SalkowskiGalilean Space
CLC number: 51A05, 53A35

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 31239-31251
DOI: 10.3934/math.20241506

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Elzawy M, Mosa S. A novel method for Mannheim curves in the Galilean 3−space G3. AIMS Mathematics, 2024, 9(11): 31239-31251. https://doi.org/10.3934/math.20241506

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Received: 04 August 2024
Revised: 14 October 2024
Accepted: 28 October 2024
Published: 04 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)