Null 2-type hypersurfaces in Euclidean 6-space

Abstract

In this paper, we study null 2-type hypersurfaces in the Euclidean space \(E^{6}\) whose second fundamental form has constant norm. We prove that every such null 2-type hypersurface in \(E^{6}\) with at most four distinct principal curvatures must be of constant mean curvature. Moreover, it has constant scalar curvature.