Geodesic
On automorphisms of CR-submanifolds of complex Hilbert space
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 126-140.

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

It is shown that there exists only one tolally nondegenerate CR manifold of type $(n,\infty)$ (up to the formal equivalence), and the dimension of its Lie algebra $\mathfrak{g}_{+}$ of positively graded formal tangent vector fields is infinite. Examples of manifolds of type $(n,\infty)$ with algebras of any given in advance finite dimension are presented.
Keywords: CR manifold, automorphisms, totally nondegenerate manifold. 
@article{SEMR_2020_17_a125,
     author = {M. A. Stepanova},
     title = {On automorphisms of {CR-submanifolds} of complex {Hilbert} space},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {126--140},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a125/}
}
TY  - JOUR
AU  - M. A. Stepanova
TI  - On automorphisms of CR-submanifolds of complex Hilbert space
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 126
EP  - 140
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a125/
LA  - ru
ID  - SEMR_2020_17_a125
ER  - 
%0 Journal Article
%A M. A. Stepanova
%T On automorphisms of CR-submanifolds of complex Hilbert space
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 126-140
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a125/
%G ru
%F SEMR_2020_17_a125
M. A. Stepanova. On automorphisms of CR-submanifolds of complex Hilbert space. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 126-140. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a125/

[1] V.K. Beloshapka, “Real submanifolds in complex space: their polynomial models, automorphisms, and classification problems”, Russ. Math. Surv., 57:1 (2002), 1–41 | DOI | MR | Zbl

[2] V.K. Beloshapka, “Universal models for real submanifolds”, Math. Notes, 75:4 (2004), 475–488 | DOI | MR | Zbl

[3] V.K. Beloshapka, “On holomorphic transformations of a quadric”, Math. USSR, Sb., 72:1 (1992), 189–205 | DOI | MR | Zbl

[4] R.V. Gammel', I.G. Kossovskii, “The envelope of holomorphy of a model third-degree surface and the rigidity phenomenon”, Proc. Steklov Inst. Math., 253 (2006), 22–36 | DOI | MR | Zbl

[5] Jan Gregorovic, On the Beloshapka's rigidity conjecture for real submanifolds in complex space, arXiv: 1807.03502

[6] M. Sabzevari, A. Spiro, On the geometric order of totally nondegenerate CR manifolds, arXiv: 1807.03076

[7] V.K. Beloshapka, “Model-surface method: an infinite-dimensional version”, Proc. Steklov Inst. Math., 279 (2012), 14–24 | DOI | MR | Zbl

[8] V.K. Beloshapka, “On the dimension of the group of automorphisms of an analytic hypersurface”, Math. USSR, Izv., 14:2 (1980), 223–245 | DOI | MR | Zbl

[9] A.B. Sukhov, “On transformations of analytic CR-structures”, Izv. Math., 67:2 (2003), 303–332 | DOI | MR | Zbl

[10] H. Cartan, Differentsialnoe ischislenie. Differentsialnye formy, Mir, M., 1971 | Zbl

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

[12] A.V. Loboda, “Sphericity of rigid hypersurfaces in $C^2$”, Math. Notes, 62:3 (1997), 329–349 | DOI | MR | Zbl