Ruled invariants and associated ruled surfaces of a space curve in galilean space

The aim of this study is to obtain the ruled invariants of the ruled surfaces in the Galilean space G_3 , which take a curve on the surface of the Galilean unit sphere as the base curve. For this purpose, first the orthonormal framework and derivative equations of the curve on the Galilean unit sphere surface are calculated. Then, by defining the structure functions and regle invariants of the regle surfaces in the Galilean sense, the regle invariants of the regle surfaces that take the spherical curve as the base curve in Galilean G_3 space are obtained.