A novel method for Mannheim curves in the Galilean $3-$space $G_3$

Abstract

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.

Keywords

• mannheim curves
• slant helices
• salkowski curves
• curves of anti-salkowski
• galilean space