On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci
Abstract
A connected real analytic hypersurface M in 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.
Domains
Mathematics [math]
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