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

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

2008-12-14

arxiv.org/abs/0812.2644v1

Mathematics

Differential Geometry

Paper accepted to publication in Manuscripta Mathematica

Scientific paper

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.

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