Geodesic
Affine and Holomorphic Equivalence of Tube Domains in $\mathbb C^2$
Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 670-682.

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It is shown that, except for several explicitly described cases, two hyperbolic tube domains in $\mathbb C^2$ are biholomorphically equivalent if and only if they are affinely equivalent. 
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N. G. Kruzhilin; P. A. Soldatkin. Affine and Holomorphic Equivalence of Tube Domains in $\mathbb C^2$. Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 670-682. http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a3/

[1] Yang P. C., “Automorphisms of tube domains”, Amer. J. Math., 104:5 (1982), 1005–1024 | DOI | MR | Zbl

[2] Shimizu S., “Automorfisms and equivalence of tube domains with bounded base”, Math. Ann., 315 (1999), 295–320 | DOI | MR | Zbl

[3] Shimizu S., “A classification of two-dimensional tube domains”, Amer. J. Math., 122 (2000), 1289–1308 | DOI | MR | Zbl

[4] Soldatkin P. A., “Golomorfnaya ekvivalentnost oblastei Reinkharta v $\mathbb C^2$”, Izv. RAN. Ser. matem., 66:6 (2002), 187–222 | MR | Zbl

[5] Kobayashi S., Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, 1970 | Zbl

[6] Kaup W., “Reele Transformationgruppen und invariante metriken auf komplexen raumen”, Invent. Math., 3 (1967), 43–70 | DOI | MR | Zbl

[7] Nakajima K., “Homogeneous hyperbolic manifolds and homogeneous Siegel domains”, J. Math. Kyoto Univ., 25:2 (1985), 269–291 | MR | Zbl

[8] Kruzhilin N. G., “Avtomorfizmy giperbolicheskikh oblastei Reinkharta”, Izv. AN SSSR. Ser. matem., 52:1 (1988), 16–40 | MR | Zbl

[9] Eastwood A., “A propos des varietés hyperboliques complètes”, C.R. Acad. Sc. Paris, 280 (1975), 1071–1074 | MR | Zbl

[10] Arnold V. A., Obyknovennye differentsialnye uravneniya, Nauka, M., 1974

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