On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci

A connected real analytic hypersurface 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 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 . Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any.