Roller coasters are usual examples of energy transformation, with an interaction of kinetic and potential energy as the train moves surrounding the curves, loops, hills and valleys of the path.. A roller coaster path so that a particle moving in space will stay on a given curve in space. The roller coaster surface is a special type of spherical surfaces. In this study, ℜ-Roller Coaster surfaces with Ribbon frame is investigate in Euclidean 3-space. Moreover, the Gaussian curvature, mean curvature, first and second fundamental form of coefficients of Roller Coaster surfaces of are examined. Then, the parallel surfaces of ℜ-Roller Coaster surfaces of are obtained. Finally, we derive the related equations for the inextensible flow of a ℜ -Roller Coaster surface.
}, number={2}, publisher={Bitlis Eren Üniversitesi} }