Minimal hypersurfaces with zero Gauss-Kronecker curvature

2004/11/29 by T. Hasanis, Hasanis, T., A. Savas-Halilaj +3
Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.math/0411627

7 pages

arxiv created 2004/11/29 · arxiv updated 2009/12/01

Abstract

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.

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