Geodesic
Holomorphic classification of four-dimensional surfaces in~$\mathbb C^3$
Izvestiya. Mathematics , Tome 72 (2008) no. 3, pp. 413-427

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

We use the method of model surfaces to study real four-dimensional submanifolds of $\mathbb C^3$. We prove that the dimension of the holomorphic symmetry group of any germ of an analytic four-dimensional manifold does not exceed 5 if this dimension is finite. (There are only two exceptional cases of infinite dimension.) The envelope of holomorphy of the model surface is calculated. We construct a normal form for arbitrary germs and use it to give a holomorphic classification of completely non-degenerate germs. It is shown that the existence of a completely non-degenerate CR-structure imposes strong restrictions on the topological structure of the manifold. In particular, the four-sphere $S^4$ admits no completely non-degenerate embedding into a three-dimensional complex manifold. 
@article{IM2_2008_72_3_a0,
     author = {V. K. Beloshapka and V. V. Ezhov and G. Schmalz},
     title = {Holomorphic classification of four-dimensional surfaces in~$\mathbb C^3$},
     journal = {Izvestiya. Mathematics },
     pages = {413--427},
     publisher = {mathdoc},
     volume = {72},
     number = {3},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a0/}
}
TY  - JOUR
AU  - V. K. Beloshapka
AU  - V. V. Ezhov
AU  - G. Schmalz
TI  - Holomorphic classification of four-dimensional surfaces in~$\mathbb C^3$
JO  - Izvestiya. Mathematics 
PY  - 2008
SP  - 413
EP  - 427
VL  - 72
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a0/
LA  - en
ID  - IM2_2008_72_3_a0
ER  - 
%0 Journal Article
%A V. K. Beloshapka
%A V. V. Ezhov
%A G. Schmalz
%T Holomorphic classification of four-dimensional surfaces in~$\mathbb C^3$
%J Izvestiya. Mathematics 
%D 2008
%P 413-427
%V 72
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a0/
%G en
%F IM2_2008_72_3_a0
V. K. Beloshapka; V. V. Ezhov; G. Schmalz. Holomorphic classification of four-dimensional surfaces in~$\mathbb C^3$. Izvestiya. Mathematics , Tome 72 (2008) no. 3, pp. 413-427. http://geodesic.mathdoc.fr/item/IM2_2008_72_3_a0/