On propagation of sphericity of real analytic hypersurfaces across Levi degenerate loci (Q1736418)

Summary: A connected real analytic hypersurface \(M \subset \mathbb{C}^{n + 1}\) 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.