https://universite-paris-saclay.hal.science/hal-03286268Merker, JoëlJoëlMerkerLMO - Laboratoire de Mathématiques d'Orsay - UP11 - Université Paris-Sud - Paris 11 - CNRS - Centre National de la Recherche ScientifiqueOn Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate LociHAL CCSD2017[MATH] Mathematics [math]MERKER, Joël2021-07-14 09:28:542023-03-24 14:53:222021-07-16 17:48:38enJournal articleshttps://universite-paris-saclay.hal.science/hal-03286268/document10.1155/2017/1314874application/pdf1A 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.