Segre varieties and Lie symmetries
نویسنده
چکیده
We show that biholomorphic automorphisms of a real analytic hypersurface in I C 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.
منابع مشابه
Segre varieties , CR geometry and Lie symmetries of second order PDE systems
We establish a link between the CR geometry of real analytic submanifolds in I C and the geometric PDE theory. The main idea of our approach is to consider biholomorphisms of a Levi-nondegenerate real analytic Cauchy-Riemann manifold M as poinwise symmetries of a second order holomorphic PDE system defining the Segre family of M. This allows to employ the well-elaborated PDE tools in order to s...
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