Geodesic
Holomorphic Maps of Levi-Degenerate Tube Hypersurfaces in $\mathbb C^3$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 183-193

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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.
Mots-clés : tube hypersurface
Keywords: holomorphic map, Levi form, complex line. 
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     author = {N. G. Kruzhilin},
     title = {Holomorphic {Maps} of {Levi-Degenerate} {Tube} {Hypersurfaces} in $\mathbb C^3$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {183--193},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_311_a9/}
}
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N. G. Kruzhilin. Holomorphic Maps of Levi-Degenerate Tube Hypersurfaces in $\mathbb C^3$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 183-193. http://geodesic.mathdoc.fr/item/TM_2020_311_a9/