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 t...
- 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
| Summary: | 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. |
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