Geodesic
Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$
Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 246-265

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A general approach to describing affine-homogeneous hypersurfaces in the space $\mathbb C^3$ is proposed. In the 2-dimensional strictly pseudoconvex (SPC) case, within the framework of such an approach, the classification problem is solved for three separate classes constituting the whole set of manifolds under consideration. One of these is the class of surfaces of tube type.
Keywords: affine-homogeneous hypersurface of tube type, Lie algebra, 5-dimensional algebra, affine vector field. 
@article{MZM_2013_94_2_a8,
     author = {T. T. D. Nguen},
     title = {Affine-Homogeneous {Real} {Hypersurfaces} of {Tube} {Type} in~$\mathbb{C}^{3}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {246--265},
     publisher = {mathdoc},
     volume = {94},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/}
}
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T. T. D. Nguen. Affine-Homogeneous Real Hypersurfaces of Tube Type in~$\mathbb{C}^{3}$. Matematičeskie zametki, Tome 94 (2013) no. 2, pp. 246-265. http://geodesic.mathdoc.fr/item/MZM_2013_94_2_a8/