Geometrical Analysis of Osculating Curves in Minkowski Space 𝔼14

This study investigates the space-like and time-like osculating curves in four-dimensional Minkowski space, [Formula: see text]. We establish necessary and sufficient conditions for a space-like or time-like curve to be congruent to an osculating curve by deriving relationships between their curvature functions. As a special case, we obtain a curvature relation for a space-like curve with a space-like principal normal vector. Furthermore, we examine cases where two curvatures are constant and derive additional relationships between the curvatures and the various components of space-like and time-like osculating curves.