Geodesic
On envelopes of holomorphy of model manifolds
Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 545-571.

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We construct envelopes of holomorphy for model manifolds of order 4 and describe a class of such manifolds whose envelope is a cylindrical domain (with respect to certain variables) based on a Siegel domain of the second kind. This enables us to prove the holomorphic rigidity of model manifolds of this class. We also study the envelope of holomorphy of a special model manifold of type (1,4) and show it to be a domain of ounded type whose distinguished boundary coincides with the initial manifold. The holomorphic automorphism group of this domain coincides with that of the initial manifold. The envelope of holomorphy is fibred into orbits of this group. The generic orbits are 8-dimensional homogeneous non-spherical completely non-degenerate manifolds in $\mathbb C^5$. 
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I. G. Kossovskii. On envelopes of holomorphy of model manifolds. Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 545-571. http://geodesic.mathdoc.fr/item/IM2_2007_71_3_a5/

[1] V. K. Beloshapka, “Universalnaya model veschestvennogo podmnogoobraziya”, Matem. zametki, 75:4 (2004), 507–522 | MR | Zbl

[2] T. Bloom, I. Graham, “On ‘type’ conditions for generic real submanifolds of $\mathbb C^n$”, Invent. Math., 40:3 (1997), 217–243 | DOI | MR | Zbl

[3] V. K. Beloshapka, “Veschestvennye podmnogoobraziya kompleksnogo prostranstva: ikh polinomialnye modeli, avtomorfizmy i problemy klassifikatsii”, UMN, 57:1 (2002), 3–44 | MR | Zbl

[4] V. K. Beloshapka, Teorema vlozheniya, http://www.strogino.ru/ṽkb/articles/teorema_vlozhenija.pdf

[5] V. K. Beloshapka, “Kubicheskaya model veschestvennogo mnogoobraziya”, Matem. zametki, 70:4 (2001), 503–519 | MR | Zbl

[6] I. Naruki, “Holomorphic extention problem for standard real submanifolds of second kind”, Publ. Res. Inst. Math. Sci., 6:1 (1970), 113–187 | DOI | MR | Zbl

[7] I. I. Pyatetskii-Shapiro, Geometriya klassicheskikh oblastei i teoriya avtomorfnykh funktsii, Fizmatgiz, M., 1961 ; I. I. Pyateskii-Shapiro, Automorphic functions and the geometry of classical domains, Math. Appl., 8, Gordon and Breach, New York–London–Paris, 1969 | Zbl | MR | Zbl

[8] R. V. Gammel, I. G. Kossovskii, “Obolochka golomorfnosti modelnoi poverkhnosti stepeni tri i fenomen zhestkosti”, Kompleksnyi analiz i prilozheniya, Tr. MIAN, 253, Nauka, M., 2006, 30–45 | MR

[9] A. E. Tumanov, “Prodolzhenie CR-funktsii v klin”, Matem. sb., 181:7 (1990), 951–964 ; A. E. Tumanov, “Extension of CR-functions into a wedge”, Math. USSR-Sb., 70:2 (1991), 385–398 | MR | Zbl | DOI

[10] V. K. Beloshapka, “Polinomialnye modeli veschestvennykh mnogoobrazii”, Izv. RAN. Ser. matem., 65:4 (2001), 3–20 | MR | Zbl

[11] B. V. Shabat, Vvedenie v kompleksnyi analiz. Ch. 2. Funktsii neskolkikh peremennykh, 3-e izd., Nauka, M., 1985 ; B. V. Shabat, Introduction to complex analysis. Part II. Functions of several variables, Transl. Math. Monogr., 110, Amer. Math. Soc., Providence, RI, 1992 | MR | Zbl | MR | Zbl

[12] E. N. Shananina, Polinomialnye modeli veschestvenno-analiticheskikh mnogoobrazii i algebry ikh avtomorfizmov, Dis. ... kand. fiz.-matem. nauk, MGU, M., 2006

[13] V. K. Beloshapka, “Moduli space of model real submanifolds”, Russ. J. Math. Phys., 13:3 (2006), 245–252 | DOI | MR | Zbl

[14] L. Khermander, Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 ; L. Hörmander, An introduction to complex analysis in several variables, D. Van Nostrand Co., Princeton–Toronto–London, 1966 | MR | Zbl | MR | Zbl

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

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

[17] G. Fels, W. Kaup, CR-manifolds of dimension 5: A Lie algebra approach, arXiv: math.DS/0508011 | MR

[18] S. N. Shevchenko, “Opisanie algebry infinitezimalnykh avtomorfizmov kvadrik korazmernosti dva i ikh klassifikatsiya”, Matem. zametki, 55:5 (1994), 142–153 | MR | Zbl

[19] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1964 ; V. S. Vladimirov, Methods of the theory of functions of many complex variables, The M. I. T. Press, Cambridge–London, 1966 | MR | Zbl | MR