Examples of scalar-flat hypersurfaces in ${\mathbb{R}}^{n+1}$

Abstract

Given a hypersurface $M$ of null scalar curvature in the unit sphere ${\mathbb{S}}^n$, $n\ge 4$, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in $\Rr^{n+1}$ as a normal graph over a truncated cone generated by $M$. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.

Paper accepted to publication in Manuscripta Mathematica