On geometry of the parallel surface of the tube surface given by the Flc frame in Euclidean 3-space

Abstract

In this study, first, the parallel surfaces of the tube surfaces given with the Flc frame are defined. By calculating the Gaussian and mean curvatures of these parallel surfaces, it was found the conditions developable and minimal. Afterwards, the conditions for parameter curves on the parallel surface to be asymptotic, geodesic and curvature lines were investigated. It has been proven that the tube and parallel tube surface preserve the Gaussian transform. Finally, examples of these surfaces are given.