Involute-evolute curves with modified orthogonal frame in Galilean space $G_{3}$

UDC 514 We introduce and study an involute-evolute curve pair within a modified orthogonal frame in the context of 3-dimensional Galilean space $G_3$. The proposed methodology involves the investigation of the aforementioned curve pair with respect to a modified orthogonal frame, specifically by analyzing their curvature and torsion properties. By using this approach, we derive various characterizations of these curves. The proposed findings contribute to the deeper understanding of the geometric properties and the behavior of involute-evolute curve pairs in the Galilean space, thereby offering potential applications in the differential geometry and mathematical physics.