In this study, 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 three dimensional Minkowski space. Moreover, we obtained that these surfaces are minimal. An addition, if these surfaces have the same Gauss map, we can determine them.
J. Math. Kyoto Univ.
46(1):
47-63
(2006).
DOI: 10.1215/kjm/1250281796