Helicoidal hypersurfaces in the four dimensional minkowski space

Abstract

Helicoidal hypersurfaces in the four dimensional Minkowski space are defined. There are three types, depending on the axis of rotation. Equations for the Gaussian and mean curvature are derived and many examples of the various types of hypersurfaces are given. A theorem classifying the helicoids with timelike axes and ΔH=AH is obtained.