Bour's theorem in minkowski 3 space

Abstract

In three dimensional Minkowski space, we show that a generalized helicoid with null axis is isometric to a rotation surface with null axis so that helices on the helicoid correspond to parallel circles on the rotation surface. In addition, if these surfaces have the same Gauss map, we can determine them. Moreover, if these surfaces with the same Gauss map are maximal, we obtained them.