Minimal hypersurfaces with zero Gauss-Kronecker curvature

Details Minimal hypersurfaces with zero Gauss-Kronecker curvature Minimal hypersurfaces with zero Gauss-Kronecker curvature

2004-11-29

arxiv.org/abs/math/0411627v1

Mathematics

Differential Geometry

7 pages

Scientific paper

We investigate complete minimal hypersurfaces in the Euclidean space $% \ {R}^{4}$, 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.

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