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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.
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https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03286268
Contributor : Joël Merker Connect in order to contact the contributor
Submitted on : Wednesday, July 14, 2021 - 9:28:54 AM
Last modification on : Saturday, July 17, 2021 - 3:31:12 AM
Long-term archiving on: : Friday, October 15, 2021 - 4:08:33 PM

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Joël Merker. On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci. Journal of Complex Analysis, Hindawi, 2017, 2017, pp.1314874. ⟨10.1155/2017/1314874⟩. ⟨hal-03286268⟩

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