Minimal hypersurfaces with zero Gauss-Kronecker curvature

Abstract

We investigate complete minimal hypersurfaces in the Euclidean space , with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^3\to R^4$ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below, then $f(M^3)$ splits as a Euclidean product $L^2\times R$, where $L^2$ is a complete minimal surface in $R^3$ with Gaussian curvature bounded from below.

7 pages