Complete and Stable O(p+1)×O(q+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space ℝ p+q+2 |
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Authors: | Jocelino Sato Vicente Francisco De Souza Neto |
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Affiliation: | (1) Faculdade de Matemática, Universidade Federal de Uberlândia, 38400-902 Uberlândia, Brazil;(2) Departamento de Matemática, Universidade Católica de Pernambuco, Rua do Principe 526, Recife, Brazil |
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Abstract: | We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝ p+q+2, p,q > 1, analyzing whether they are embedded and stable. The Morse index of the complete hypersurfaces show the existence of embedded, complete and globally stable zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in ℝ p+q+2, p+q≥ 7, which are not homeomorphic to ℝ p+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature. Mathematics Subject Classifications (2000): 53A10, 53C42,49005. |
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Keywords: | equivariant geometry scalar curvature stability Bernstein's conjecture |
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