Minimal hypersurfaces with zero Gauss-Kronecker curvature

الأصل · EN

We investigate complete minimal hypersurfaces in the Euclidean space % R⁴, with Gauss-Kronecker curvature identically zero. We prove that, if f:M³→ R⁴ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature bounded from below, then f(M³) splits as a Euclidean product L²× R, where L² is a complete minimal surface in R³ with Gaussian curvature bounded from below.