This research presents a novel method for Mannheim curves in three-dimensional Galilean space $ G_3$. Using this method, the necessary and sufficient conditions, along with the established results, must be satisfied for a curve in $ G_3$ 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 $ G_3$, the Mannheim partner curves are described.
Citation: Mervat Elzawy, Safaa Mosa. A novel method for Mannheim curves in the Galilean $3-$space $G_3$[J]. AIMS Mathematics, 2024, 9(11): 31239-31251. doi: 10.3934/math.20241506
This research presents a novel method for Mannheim curves in three-dimensional Galilean space $ G_3$. Using this method, the necessary and sufficient conditions, along with the established results, must be satisfied for a curve in $ G_3$ 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 $ G_3$, the Mannheim partner curves are described.
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Mervat Elzawy, Safaa Mosa. A novel method for Mannheim curves in the Galilean $3-$space $G_3$[J]. AIMS Mathematics, 2024, 9(11): 31239-31251. doi: 10.3934/math.20241506
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