On propagation of sphericity of real analytic hypersurfaces across Levi degenerate loci
type: Item
instance of: scholarly article
title: On propagation of sphericity of real analytic hypersurfaces across Levi degenerate loci
zbMATH Open document ID: 1416.32005
DOI: 10.1155/2017/1314874
author: Joël Merker
published in: Journal of Complex Analysis
publication date: 2019-03-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32C07
Mathematics Subject Classification ID: 32V40
zbMATH DE Number: 7042057
zbMATH Keywords: real anlytic hypersuface
zbMATH Keywords: nondegenerate Levi form
Wikidata QID: Q59145697
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1314874
OpenAlex ID: W2598354976
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description: scientific article; zbMATH DE number 7042057