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 Trudy Mat. Inst. Steklova, 2020, Volume 311, Pages 183–193 (Mi tm4123)

Holomorphic Maps of Levi-Degenerate Tube Hypersurfaces in $\mathbb C^3$

N. G. Kruzhilin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: Locally biholomorphic maps between 2-nondegenerate smooth real tube hypersurfaces in $\mathbb C^3$ with Levi form of rank $1$ are described. It is shown that, except for hypersurfaces that are locally equivalent to the boundary of the future tube, such maps must be affine. The proof uses the local holomorphic version of the fundamental theorem of projective geometry which was earlier proved by the author.

 Funding Agency Grant Number Russian Science Foundation 19-11-00316 This work is supported by the Russian Science Foundation under grant 19-11-00316.

DOI: https://doi.org/10.4213/tm4123

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 311, 171–179

Bibliographic databases:

UDC: 517.55
Revised: May 2, 2020
Accepted: May 30, 2020

Citation: N. G. Kruzhilin, “Holomorphic Maps of Levi-Degenerate Tube Hypersurfaces in $\mathbb C^3$”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 183–193; Proc. Steklov Inst. Math., 311 (2020), 171–179

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm4123
• https://doi.org/10.4213/tm4123
• http://mi.mathnet.ru/eng/tm/v311/p183

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