Stable minimal cones in ℝ8 and ℝ9 with constant scalar curvature

In this paper we prove that if M ⊏ ℝn , n = 8 or n = 9, is a n  - 1 dimensional stable minimal complete cone such that its scalar curvature varies radially, then M must be either a hyperplane or a Clifford minimal cone. By Gauss' formula, the condition on the scalar curvature is equivalent to the condition that the function K1(m)2 + ... + Kn-1 (m)2 varies radially. Here the Ki are the principal curvatures at m ∈ M. Under the same hypothesis, for M ⊏ ℝ10  we prove that if not only K1(m)2 + ... + Kn-1 (m)2   varies radially but either K1(m)3 + ... + Kn-1 (m)3 varies radially or K1(m)4 + ... + Kn-1 (m)4 varies radially, then M must be either a hyperplane or a Clifford minimal cone.

• Autores: Perdomo, Oscar
• Tipo de recurso: Article of journal
• Fecha de publicación: 2002
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/43808
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/43808; http://bdigital.unal.edu.co/33906/
• Palabra clave: Clifford hypersurfaces; minimal hypersurfaces; shape operator
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional