Abstract
Equivariant geometry methods are used to study and classify zero scalarcurvature O(p + 1) × O(p + 1)-invariant hypersurfaces in ℝ2p + 2with p > 1. First of all the O(p + 1) × O(p + 1)-invariant hypersurfaces are classified according to their profile curves, and it is shown that there are complete and embedded examples. Next the Morse index of the complete examples is studied, in particular, it is proved that there exist globally stable examples.These stable examples provide counter-examples, in odddimensions greater than or equal to nine, to a Bernstein-type conjecture in the stable class, for immersions with zero scalar curvature.
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Sato, J. Stability of O(p + 1) × O(p + 1)-Invariant Hypersurfaces with Zero Scalar Curvature in Euclidean Space. Annals of Global Analysis and Geometry 22, 135–153 (2002). https://doi.org/10.1023/A:1019536730847
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DOI: https://doi.org/10.1023/A:1019536730847