Minimal hypersurfaces in $\mathbb{S}^5$ with vanishing Gauss-Kronecker   curvature
  In this paper we present a local description for complete minimal hypersurfaces in $\mathbb{S}^5$ with zero Gauss-Kronecker curvature, zero $3$-mean curvature and nowhere zero second fundamental form. 
M. M. Diniz, J. A. M. Vilhena, J. F. Z. Zapata
math.DG