Circular surfaces produced from FLC frame geometry

Our study is organized in five sections. In the introduction section, the main purpose of the study, the studies carried out were included and the reason for addressing the subject was discussed. In the Materials and Methods section, Euclidean space, polynomial curves, Flc frame formulas, basic concepts of the Flc frame and their theories are summarized. In the third chapter, the geometric properties of a tube surface given by the Flc frame in Euclidean space, which is the main purpose of this study, were examined. The conditions for the parameter curves lying on this surface to be geodesic curves, asymptotic curves and curvature lines were investigated. Afterwards, the focal surfaces and parallel surfaces of these tube surfaces were examined and the geometric properties of these surfaces were examined. By finding the geometric properties of the obtained surfaces, it was investigated whether the parameter curves lying on the surface were special curves. Then, Roller coaster surfaces were expressed according to the Flc frame and the relationship between them and ruled surfaces was given. The conditions for Roller coaster surfaces to be developable and minimal were investigated. Striction curves were obtained by finding the geometric location of the singular points of this surface. Visual expressions of all obtained surfaces were given. While the results and recommendations are given in the fourth section, the sources used are included in the last section.