Common special curve regulated surface families

The surface formed by the movement of a line along a curve is called a ruled surface. Since ruled surfaces are a special case of generalized surfaces, they have a single defined curve. This curve is also called the stricture curve. In this study, the characterizations of the asymptotic normal surface from the g asymptotic normal vector during the formation of the surface created by the global indicator vector e were examined. First, the ruled surface family is defined by the common stricture curve. Using the geodesic Frenet framework of the ruled surface , the necessary conditions for this striction curve to be a geodesic, curvature line and asymptotic curve are presented. Finally, some examples are given to show ruled surfaces with common geodesic, curvature line and asymptotic curve. Suggestions were made for future studies.