Examples of scalar-flat hypersurfaces in $\mathbb{R}^{n+1}$
| Autor: | Marc Soret, Jorge H. de Lira |
|---|---|
| Přispěvatelé: | Laboratoire d'Imagerie Fonctionnelle (LIF), Université Pierre et Marie Curie - Paris 6 (UPMC)-IFR14-IFR49-Institut National de la Santé et de la Recherche Médicale (INSERM), Nuclear Medicine Department, HIA Val-de-Grâce, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Unit sphere
Mathematics - Differential Geometry General Mathematics Second fundamental form 010102 general mathematics Mathematical analysis Scalar (mathematics) Algebraic geometry 53C42 01 natural sciences Graph 010101 applied mathematics Combinatorics Number theory Hypersurface Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] FOS: Mathematics Mathematics::Differential Geometry 0101 mathematics Mathematics Scalar curvature |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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