On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci. (28th March 2017)

• Record Type: Journal Article
• Authors: Merker, Joël
• Other Names: Tomassini Giuseppe Academic Editor.
• Is Part Of: Journal of complex analysis. Volume 2017(2017)
• Publication Date: 2017-03-28
• Subjects: Functions of complex variables -- Periodicals; Mathematical analysis -- Periodicals; 515.905
• DOI: 10.1155/2017/1314874
• Languages: English
• ISSNs: 2314-4963

Abstract

Abstract : A connected real analytic hypersurface M ⊂ 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.