Geodesic
Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups
Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 114-142

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A local classification is constructed for real nonumbilic hypersurfaces of three-dimensional complex spaces that have sign-indefinite nondegenerate Levi forms and admit seven-dimensional transitive groups of local holomorphic transformations. A full (up to holomorphic equivalence) explicit description of such manifolds is presented. The basic tool used in this paper is the apparatus of local normal forms for the equations of the manifolds considered. 
@article{TRSPY_2001_235_a8,
     author = {A. V. Loboda},
     title = {Homogeneous {Real} {Hypersurfaces} in $\mathbb C^3$ with {Two-Dimensional} {Isotropy} {Groups}},
     journal = {Informatics and Automation},
     pages = {114--142},
     publisher = {mathdoc},
     volume = {235},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2001_235_a8/}
}
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A. V. Loboda. Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups. Informatics and Automation, Analytic and geometric issues of complex analysis, Tome 235 (2001), pp. 114-142. http://geodesic.mathdoc.fr/item/TRSPY_2001_235_a8/