Geodesic
Homogeneous strictly pseudoconvex hypersurfaces in~$\mathbb C^3$ with two-dimensional isotropy groups
Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1741-1761

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Strictly pseudoconvex non-spherical hypersurfaces in 3-dimensional complex space that are homogeneous with respect to local Lie groups of holomorphic transformations are studied. The author proved earlier that a Lie group $\operatorname{Aut}M$ acting transitively on such a manifold $M$ has dimension at most 7. A complete list of homogeneous surfaces such that $\operatorname{Aut}M$ has dimension precisely 7 (and the corresponding isotropy subgroup has dimension precisely 2) is given. The main tools used in the paper are local normal equations describing the manifolds under consideration. 
@article{SM_2001_192_12_a0,
     author = {A. V. Loboda},
     title = {Homogeneous strictly pseudoconvex hypersurfaces in~$\mathbb C^3$ with two-dimensional isotropy groups},
     journal = {Sbornik. Mathematics},
     pages = {1741--1761},
     publisher = {mathdoc},
     volume = {192},
     number = {12},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_12_a0/}
}
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A. V. Loboda. Homogeneous strictly pseudoconvex hypersurfaces in~$\mathbb C^3$ with two-dimensional isotropy groups. Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1741-1761. http://geodesic.mathdoc.fr/item/SM_2001_192_12_a0/