Null scrolls with spacelike harmonic evolutes in Lorentz-Minkowski space

Null scrolls in Lorentz-Minkowski space are ruled surfaces whose rulings are null vectors. They are the only surfaces whose harmonic evolute is not a surface, but a single curve which is spacelike if the mean curvature of a null scroll is not constant. In this paper we do the inverse problem: given a spacelike curve, we find null scrolls having this curve as its harmonic evolute. We also discuss in which cases a null scroll is a B-scroll.