On admissible curves and their evolution equations in pseudo-Galilean space

Abstract

The evolution equations of some forms of admissible curves in the pseudo-Galilean Space \(G_{3}^1\) are investigated in this paper. In more detail, we use two separate methods to obtain coupled nonlinear partial differential equations of time evolution in terms of their curvatures. The first method studies the evolution equations for admissible curves via the frame field, while the second studies the evolution equations via the velocity vector. Then, the position vectors of the evolving curves are formulated. Also, we conduct comparative research of the evolution equations for curves in different spaces. We furthermore present some models as an application of the evolution equations of the curvature and torsion for admissible curves, confirming our theoretical results.