Geodesic
On transformations of analytic CR-structures
Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 303-332

Voir la notice de l'article provenant de la source Math-Net.Ru

We establish a link between the CR-geometry of real-analytic submanifolds in $\mathbb C^n$ and the geometry of differential equations. The idea of our approach is to regard biholomorphisms of a Levi-non-degenerate real-analytic CR-manifold $\mathscr M$ as point Lie symmetries of the second-order holomorphic system of differential equations defining the Segre family of $\mathscr M$. This enables us to study the biholomorphism group of $\mathscr M$ by means of the geometric theory of differential equations. We give several examples and applications to CR-geometry: results on the finite-dimensionality of the biholomorphism group and precise estimates of its dimension, and an explicit parametrization of the Lie algebra of infinitesimal automorphisms. 
@article{IM2_2003_67_2_a4,
     author = {A. B. Sukhov},
     title = {On transformations of analytic {CR-structures}},
     journal = {Izvestiya. Mathematics },
     pages = {303--332},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a4/}
}
TY  - JOUR
AU  - A. B. Sukhov
TI  - On transformations of analytic CR-structures
JO  - Izvestiya. Mathematics 
PY  - 2003
SP  - 303
EP  - 332
VL  - 67
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a4/
LA  - en
ID  - IM2_2003_67_2_a4
ER  - 
%0 Journal Article
%A A. B. Sukhov
%T On transformations of analytic CR-structures
%J Izvestiya. Mathematics 
%D 2003
%P 303-332
%V 67
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a4/
%G en
%F IM2_2003_67_2_a4
A. B. Sukhov. On transformations of analytic CR-structures. Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 303-332. http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a4/