Helical hypersurfaces in minkowski geometry E^1_4

Abstract

We define helical (i.e., helicoidal) hypersurfaces depending on the axis of rotation in Minkowski four-space E41 . There are three types of helicoidal hypersurfaces. We derive equations for the curvatures (i.e., Gaussian and mean) and give some examples of these hypersurfaces. Finally, we obtain a theorem classifying the helicoidal hypersurface with timelike axes satisfying ΔIH=AH .