, Volume 29, Issue 3, pp 221-240
Date: 20 May 2006

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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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.