Ruled surfaces according to the Sannia frame obtained from involute curve

This thesis consists of five chapters. In the first chapter, a literature review is conducted in the introduction section, providing information about previous studies. The second chapter covers the basic concepts related to Euclidean space. The third chapter is presented under two subheadings. The first subheading includes definitions and theorems related to the involute curve. The second subheading discusses ruled surfaces with the Sannia frame. fourth chapter, which constitutes the original part of the study, is designed in three subsections. The first subsection investigates ruled surfaces formed by the tangent vector of the involute curve, the second subsection examines ruled surfaces formed by the normal vector, and the third subsection explores ruled surfaces formed by the binormal vector. Additionally, the striction curve of each ruled surface is found, and the Sannia frame defined along this curve is calculated. Subsequently, the normal vector fields, the first and second fundamental forms of each surface, and the Gaussian and mean curvatures are calculated using the coefficients of these fundamental forms. At the end of the study, the developable and minimal conditions of the surfaces are expressed as results using the Gaussian and mean curvatures. In the fifth chapter, the findings obtained from the entire study are presented, and suggestions are made for future research.