Annals of Global Analysis and Geometry

, Volume 29, Issue 3, pp 221–240

Complete and Stable O(p+1)×O(q+1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space ℝp+q+2

  • Jocelino Sato
  • Vicente Francisco De Souza Neto
Article

DOI: 10.1007/s10455-005-9006-4

Cite this article as:
Sato, J. & Neto, V.F.D.S. Ann Glob Anal Geom (2006) 29: 221. doi:10.1007/s10455-005-9006-4

Abstract

We classify the zero scalar curvature O(p+1)×O(q+1)-invariant hypersurfaces in the euclidean space ℝp+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 ℝp+q+2, p+q≥ 7, which are not homeomorphic to ℝp+q+1. Such stable examples provide counter-examples to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature.

Keywords

equivariant geometryscalar curvaturestabilityBernstein's conjecture

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Jocelino Sato
    • 1
  • Vicente Francisco De Souza Neto
    • 2
  1. 1.Faculdade de MatemáticaUniversidade Federal de UberlândiaUberlândiaBrazil
  2. 2.Departamento de MatemáticaUniversidade Católica de PernambucoRecifeBrazil