A new characterization of null scrolls as parallel surfaces

Abstract

In this paper, we present a theorem which explains the necessary onditions for parallel surfaces of null scrolls to be surfaces again. Then, we give some properties of parallel ruled surfaces such as the frame fields in terms of the original base curve’s frame vectors, the cases of cross products of these frames’ vector fields. Also, we show the parallel ruled surfaces to be developable from a different point of view. Additionally, we obtain a relation between Gauss curvatures and mean curvatures. Finally, we characterize the striction curve of the parallel ruled surface. In the example, we draw a graph for a particular null scroll and its parallel surface.