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Mathematische Zeitschrift

, Volume 238, Issue 3, pp 483–492 | Cite as

Segre varieties and Lie symmetries

  • Alexandre Sukhov

Abstract.

We show that biholomorphic automorphisms of a real analytic hypersurface in \({mathbb C}^{n+1}\) can be considered as (pointwise) Lie symmetries of a holomorphic completely overdetermined involutive second order PDE system defining its Segre family. Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of such a system and give a new proof of some well known results of CR geometry.

Keywords

Segre Variety Analytic Hypersurface Real Analytic Hypersurface Biholomorphic Automorphism Infinitesimal Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexandre Sukhov
    • 1
  1. 1.Université des Sciences et Technologies de Lille, Laboratoire d'Arithmétique – Géométrie – Analyse – Topologie, Unité Mixte de Recherche 8524, U.F.R. de Mathématique, 59655 Villeneuve d'Ascq, Cedex, France (e-mail: Alexandre.Sukhov@agat.univ-lille1.fr)FR

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