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

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.