Non-closed minimal hypersurfaces of $\Bbb{S^4}(1)$ with identically zero Gau\ss-Kronecker curvature

Abstract

We give a partial local description of minimal hypersurfaces $M^3$ with identically zero Gau\ss-Kronecker curvature function in the unit 4-sphere $\Bbb{S}^4(1)$, without assumption on the compactness of $M^3$.