Geodesic
Some invariants of tubular hypersurfaces in $\mathbb C^2$
Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 211-223.

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

Holomorphic invariants of tubular hypersurfaces (tubes) over plane analytic curves are treated. Nonspherical Levi nondegenerate tubes over affine homogeneous curves are studied. Such surfaces are shown to be holomorphically equivalent if and only if they are affinely equivalent. Two problems concerning the description of locally specified homogeneous hypersurfaces in $\mathbb C^2$ are posed. The construction of the invariants is based on the reduction of the equation of a tubular hypersurface to Moser normal form. Some properties of this reduction are discussed. 
@article{MZM_1996_59_2_a6,
     author = {A. V. Loboda},
     title = {Some invariants of tubular hypersurfaces in $\mathbb C^2$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {211--223},
     publisher = {mathdoc},
     volume = {59},
     number = {2},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a6/}
}
TY  - JOUR
AU  - A. V. Loboda
TI  - Some invariants of tubular hypersurfaces in $\mathbb C^2$
JO  - Matematičeskie zametki
PY  - 1996
SP  - 211
EP  - 223
VL  - 59
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a6/
LA  - ru
ID  - MZM_1996_59_2_a6
ER  - 
%0 Journal Article
%A A. V. Loboda
%T Some invariants of tubular hypersurfaces in $\mathbb C^2$
%J Matematičeskie zametki
%D 1996
%P 211-223
%V 59
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a6/
%G ru
%F MZM_1996_59_2_a6
A. V. Loboda. Some invariants of tubular hypersurfaces in $\mathbb C^2$. Matematičeskie zametki, Tome 59 (1996) no. 2, pp. 211-223. http://geodesic.mathdoc.fr/item/MZM_1996_59_2_a6/

[1] Blashke W., Affine Differentialgeometrie, Berlin, 1923

[2] Shirokov A. P., Shirokov P. A., Affinnaya differentsialnaya geometriya, Fizmatlit, M., 1959 | Zbl

[3] Dadok J., Yang P., “Automorphisms of tube domains and spherical hypersurfaces”, Amer. J. Math., 107:4 (1985), 999–1013 | DOI | MR | Zbl

[4] Moser J. K., “Real hypersurfaces in complex manifolds”, Acta Math., 133:3 (1974), 219–271 | MR

[5] Beloshapka V. K., “O razmernosti grupp avtomorfizmov analiticheskoi giperpoverkhnosti”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 243–266 | MR | Zbl

[6] Loboda A. V., “Linearizuemost avtomorfizmov nesfericheskikh poverkhnostei”, Izv. AN SSSR. Ser. matem., 46:4 (1982), 864–880 | MR | Zbl