Null scrolls as B-scrolls in Lorentz–Minkowski 3-space

Abstract

Null scrolls, i.e. ruled surfaces whose base curve and rulings are both lightlike (null), are Lorentzian surfaceshaving no Euclidean counterparts. In this work we present reparametrization of nondegenerate null scroll as a Bscroll,i.e. as a ruled surface whose rulings correspond to the binormal vectors of a base curve. We prove that thecurvature of a base curve, which determines the Gaussian and mean curvature of a null scroll, is invariant under such areparametrization. We also determine a one-parameter family of null curves on null scroll which serve as base curves forthis kind of reparametrization.