On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci. (28th March 2017) - Merker, Joël
Abstract : A connected real analytic hypersurface M ⊂ C n + 1 whose Levi form is nondegenerate in at least one point—hence at every point of some Zariski-dense open subset—is locally biholomorphic to the model Heisenberg quadric pseudosphere of signature ( k, n - k ) in one point if and only if, at every other Levi nondegenerate point, it is also locally biholomorphic to some Heisenberg pseudosphere, possibly having a different signature ( l, n - l ) . Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any.