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

Jorge H. S. de Lira; Marc Soret

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arXiv · 0812.2644

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

Jorge H. S. de Lira·Marc Soret

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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.

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BibTeX RIS

Jorge H. S. de Lira, Marc Soret. 2008-12-14. Examples of scalar-flat hypersurfaces in $\mathbb{R}^{n+1}$. https://arxiv.org/abs/0812.2644

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