|Revista Colombiana de Matemáticas|
(2002)Páginas 97 - 106
Abstract. 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 1(m)2 + · · · + n-1(m)2 varies radially. Here the i are the principal curvatures at m M . Under the same hypothesis, for M R10 we prove that if not only 1(m)2 + · · · + n-1(m)2 varies radially but either 1(m)3 + · · · + n-1(m)3 varies radially or 1(m)4 + · · · + n-1(m)4 varies radially, then M must be either a hyperplane or a Clifford minimal cone.Palabras claves. Clifford hypersurfaces, minimal hypersurfaces, shape operator.