Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature (Q909264)

The structure of minimal hypersurfaces in the four-sphere with vanishing Gauss-Kronecker curvature is studied. A technique of de Almeida and Brito constructs such hypersurfaces from minimal surfaces in the four sphere satisfying a curvature condition. In this paper, their technique is extended to cover the case where the minimal surface may have branch points. A theorem that characterizes any minimal hypersurface of the four-sphere with vanishing Gauss-Kronecker curvature as coming from this construction is then established.