Geodesic
Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 246-265.

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

A general approach to describing affine-homogeneous hypersurfaces in the space $\mathbb C^3$ is proposed. In the 2-dimensional strictly pseudoconvex (SPC) case, within the framework of such an approach, the classification problem is solved for three separate classes constituting the whole set of manifolds under consideration. One of these is the class of surfaces of tube type.
Keywords: affine-homogeneous hypersurface of tube type, Lie algebra, 5-dimensional algebra, affine vector field. 
@article{MZM_2013_94_2_a8,
     author = {T. T. D. Nguen},
     title = {Affine-Homogeneous {Real} {Hypersurfaces} of {Tube} {Type} in~$\mathbb{C}^{3}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {246--265},
     publisher = {mathdoc},
     volume = {94},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/}
}
TY  - JOUR
AU  - T. T. D. Nguen
TI  - Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$
JO  - Matematičeskie zametki
PY  - 2013
SP  - 246
EP  - 265
VL  - 94
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/
LA  - ru
ID  - MZM_2013_94_2_a8
ER  - 
%0 Journal Article
%A T. T. D. Nguen
%T Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$
%J Matematičeskie zametki
%D 2013
%P 246-265
%V 94
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/
%G ru
%F MZM_2013_94_2_a8
T. T. D. Nguen. Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 246-265. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/

[1] A. V. Loboda, “Odnorodnye veschestvennye giperpoverkhnosti v $\mathbb C^3$ s dvumernymi gruppami izotropii”, Analiticheskie i geometricheskie voprosy kompleksnogo analiza, Sbornik statei. K 70-letiyu so dnya rozhdeniya akademika Anatoliya Georgievicha Vitushkina, Tr. MIAN, 235, Nauka, M., 2001, 114–142 | MR | Zbl

[2] A. V. Loboda, “Odnorodnye strogo psevdovypuklye giperpoverkhnosti v $\mathbb C^3$ s dvumernymi gruppami izotropii”, Matem. sb., 192:12 (2001), 3–24 | DOI | MR | Zbl

[3] A. V. Loboda, “Ob opredelenii odnorodnoi strogo psevdo-vypukloi giperpoverkhnosti po koeffitsientam ee normalnogo uravneniya”, Matem. zametki, 73:3 (2003), 453–456 | DOI | MR | Zbl

[4] G. Fels, W. Kaup, “Classification of Levi degenerate homogeneous CR-manifolds in dimension 5”, Acta Math., 201:1 (2008), 1–82 | DOI | MR | Zbl

[5] V. K. Beloshapka, I. G. Kossovskiy, “Classification of homogeneous CR-manifolds in dimension 4”, J. Math. Anal. Appl., 374:2 (2011), 655–672 | DOI | MR | Zbl

[6] A. V. Loboda, A. S. Khodarev, “Ob odnom semeistve affinno-odnorodnykh veschestvennykh giperpoverkhnostei 3-mernogo kompleksnogo prostranstva”, Izv. vuzov. Matem., 2003, no. 10, 38–50 | MR | Zbl

[7] A. V. Loboda, “Klassifikatsiya affinno-odnorodnykh nevyrozhdennykh po Levi veschestvennykh giperpoverkhnostei prostranstva $\mathbb C^2$”, K 100-letiyu so dnya rozhdeniya N. V. Efimova, Sovremennye problemy matematiki i mekhaniki, 6, Matematika. Vyp. 3, Izd-vo Mosk. un-ta, M., 2011, 56–68

[8] A. V. Loboda, “Affinno-odnorodnye golomorfno-ploskie giperpoverkhnosti v $\mathbb C^2$”, Materialy 10-i Kazanskoi letnei shkoly-konferentsii, Kazan, 2011, 172–173

[9] E. Cartan, “Sur la géométrie pseudoconforme des hypersurfaces de l'espace de deux variables complexes”, Ann. Math. Pura Appl. (4), 11:1 (1933), 17–90 | DOI | MR | Zbl

[10] M. S. Danilov, A. V. Loboda, “Ob affinnoi odnorodnosti indefinitnykh veschestvennykh giperpoverkhnostei prostranstva $\mathbb{C}^3$”, Matem. zametki, 88:6 (2010), 867–884 | DOI | MR

[11] V. K. Evchenko, A. V. Loboda, One Family of Affinely Homogeneous Algebraic Surfaces in $\mathbb C^3$, http://www.mathematik.uni-bielefeld.de/sfb701/files/preprints/sfb11129.pdf

[12] B. V. Shabat, Vvedenie v kompleksnyi analiz. Ch. 2. Funktsii neskolkikh peremennykh, Nauka, M., 1976 | MR | Zbl

[13] T. T. Z. Nguen, “Affinno-odnorodnye giperpoverkhnosti trubchatogo tipa v $\mathbb C^3$”, Voronezhskaya zimnyaya matematicheskaya shkola, Tezisy dokladov, Voronezh, 2011, 236–237

[14] B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Sovremennaya geometriya. Metody i prilozheniya, Nauka, M., 1979 | MR | Zbl

[15] B. Doubrov, B. Komrakov, M. Rabinovich, “Homogeneous surfaces in the three-dimensional affine geometry”, Geometry and Topology of Submanifolds, VIII, World Sci., Singapore, 1996, 168–178 | MR | Zbl

[16] M. Eastwood, V. Ezhov, “On affine normal forms and a classification of homogeneous surfaces in affine three-space”, Geom. Dedicata, 77:1 (1999), 11–69 | DOI | MR | Zbl

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

[18] P. A. Shirokov, A. P. Shirokov, Affinnaya differentsialnaya geometriya, Fizmatgiz, M., 1959 | MR | Zbl

[19] A. V. Loboda, “Vsyakaya golomorfno-odnorodnaya trubka v $C^2$ imeet affinno-odnorodnoe osnovanie”, Sib. matem. zhurn., 42:6 (2001), 1335–1339 | MR | Zbl

[20] V. K. Beloshapka, “Odnorodnye veschestvennye giperpoverkhnosti v $\mathbb C^2$”, Matem. zametki, 60:5 (1996), 760–764 | DOI | MR | Zbl

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

[22] A. V. Isaev, M. A. Mischenko, “Klassifikatsiya sfericheskikh trubchatykh giperpoverkhnostei, imeyuschikh v signature formy Levi odin minus”, Izv. AN SSSR. Ser. matem., 52:6 (1988), 1123–1153 | MR | Zbl