Ruled Surfaces Created with Spherical Curves in Pseudo-Galilean Space

This study focuses on ruled surfaces in three-dimensional pseudo-Galilean space G_3^1, where the generator vector field of these ruled surfaces is defined by a curve on the unit pseudo-Galilean sphere. Initially, the orthonormal frame and derivative equations of the curve on the pseudo-Galilean unit sphere are calculated. Conditions are provided for a unit speed curve on a unit pseudo-Galilean sphere to be curvature line, geodesic curve or asymptotic curve in the pseudo-Galilean sense. Subsequently, the structure functions and ruled invariants of the ruled surfaces are defined and obtained in the pseudo-Galilean sense. This research encompasses all three types of ruled surfaces, and the relationships between the Frenet frames of the generating curves and those of the corresponding surfaces are systematically examined.