Mathematische Zeitschrift

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

Segre varieties and Lie symmetries

  • Alexandre Sukhov


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.


Segre Variety Analytic Hypersurface Real Analytic Hypersurface Biholomorphic Automorphism Infinitesimal Symmetry 
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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:

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