Table of Contents
Journal of Complex Analysis
Volume 2017, Article ID 1314874, 8 pages
https://doi.org/10.1155/2017/1314874
Research Article

On Propagation of Sphericity of Real Analytic Hypersurfaces across Levi Degenerate Loci

Département de Mathématiques d’Orsay, Paris, France

Correspondence should be addressed to Joël Merker; rf.dusp-u.htam@rekrem.leoj

Received 29 July 2016; Accepted 19 February 2017; Published 28 March 2017

Academic Editor: Giuseppe Tomassini

Copyright © 2017 Joël Merker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A connected real analytic hypersurface 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 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 . Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any.