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.
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