Gauss image and rigidity of complete minimal hypersurfaces
Andreas Savas-Halilaj Leibniz Universität Hannover
Due to work of Dajczer and Gromoll in the mid 80's, a non-rigid complete minimal hypersurface $M^n$ in $R^{n+1}$ splits as the euclidean product $M^n=M^3\times R^{n-3}$, where here $M^3$ is a complete minimal hypersurface in $R^4$ with zero Gauss-Kronecker curvature. Hence, the problem reduces in the classification of these 3-dimensional objects. The aim of this talk is to give a complete local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. This description is given in terms of the Gauss map of the hypersurface. Moreover, we will give a classification of complete 3-dimensional minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.