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

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