Equiform rectifying curves in Galilean space G4

Abstract

This research paper presents the equiform rectifying curves in Galilean space G4, and establish the relation between equiform curves and their equiform curvature functions. The proposed methodology involves studying the necessary and sufficient conditions for the curve α(σ) with non zero curvatures K1(σ), K2(σ), and K3(σ) to be congruent to an equiform rectifying curve. By employing this approach we derive various characterizations of these curves, also deduce that there are no equiform rectifying curves in G4 with zero constant equiform curvature functions K2(σ), and K3(σ). The findings contribute to a deeper understanding of the geometric properties and behaviour of equiform rectifying curves in Galilean space G4. Thereby offering potential applications in fields such as mathematical physics and differential geometry.

Keywords

• Frenet–Serret frame
• Equiform curvature functions
• Congruent curves
• Equiform parameter
• Non linear differential equations