English

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

Differential Geometry 2008-12-16 v1

Abstract

Given a hypersurface MM of null scalar curvature in the unit sphere Sn\mathbb{S}^n, n4n\ge 4, such that its second fundamental form has rank greater than 2, we construct a singular scalar-flat hypersurface in \Rrn+1\Rr^{n+1} as a normal graph over a truncated cone generated by MM. Furthermore, this graph is 1-stable if the cone is strictly 1-stable.

Keywords

Cite

@article{arxiv.0812.2644,
  title  = {Examples of scalar-flat hypersurfaces in $\mathbb{R}^{n+1}$},
  author = {Jorge H. S. de Lira and Marc Soret},
  journal= {arXiv preprint arXiv:0812.2644},
  year   = {2008}
}

Comments

Paper accepted to publication in Manuscripta Mathematica

R2 v1 2026-06-21T11:51:52.174Z