Generalized null Cartan Mannheim mates by means of differential equations for position vectors

This study investigates generalized null Cartan Mannheim curves and their corresponding mate curves in Minkowski spacetime, with a particular focus on their relevance to theoretical physics. By characterizing null Cartan W-curves through differential equations involving their curvature functions, we uncover structural relationships that resonate with the geometric behavior of particle trajectories in relativistic way. The generalized null Mannheim twisted curves are analyzed alongside their mate curves, offering explicit descriptions of how curvature and torsion functions interrelate through position vector components. Several concrete examples are provided to illustrate the theoretical constructs.