Ruled Surfaces Constructed by the Involute-Evolute Curve with Sannia Frame

In this study, ruled surfaces generated by the tangent, normal, and binormal vectors of the involute curve are investigated. Furthermore, the striction curve of each ruled surface is determined, and the Sannia frame defined along this curve is calculated. Subsequently, the normal vector fields of each surface, the first and second fundamental forms, and the Gaussian and mean curvatures are computed using the coefficients of these fundamental forms. At the end of the study, the developability and minimality of the surfaces are evaluated as results based on their Gaussian and mean curvatures. Additionally, examples of the surfaces are provided, and their graphs are plotted.