Ruled Invariants and Ruled Surfaces Created with Spherical Curves in Galilean Space

This study aims to examine the ruled invariants of ruled surfaces in three-dimensional Galilean space G_3, where the direction vector is determined by a curve lying on the Galilean central unit sphere. The main goal is to derive ruled invariants of such surfaces by employing a geometric approach rooted in the properties of spherical curves. To achieve this, we first compute the orthonormal frame and corresponding derivative equations of a curve lying on the surface of the Galilean central unit sphere. Then, structure functions and ruled invariants are defined and obtained in Galilean geometry sense. The study covers all three types of ruled surfaces in Galilean space. Additionally, the relationships between the Frenet frames of the curves and those of the ruled surfaces are examined in a systematic manner. The findings provide insight into the intrinsic properties of ruled surfaces and contribute to the broader understanding of geometry in non-Euclidean settings.