Hipersuperfícies com curvatura escalar nula invariantes pela ação O(p+1) X O(p+1)

Abstract

We use methods of equivariant geometry to study and classify the hypersurfaces of R2p + 2 with null scalar curvature, invariant by the action of group O (p + 1) x O (p + 1), with p> 1. First we classify these hypersurfaces according to their generative curve, and we show that there are complete and immersed examples. We then study the Morse index of the full examples showing, in particular, that there are globally stable examples. These stable examples give counter-examples, in odd dimensions greater than or equal to 9, for a Bernstein conjecture, in the stable class, for immersions with zero scalar curvature.