Geodesic
Homogeneous Nondegenerate Hypersurfaces in $\mathbb{C}^3$ with Two-Dimensional Isotropy Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 80-83

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We construct a complete list of nonspherical real hypersurfaces in $\mathbb{C}^3$ that are Levi nondegenerate and admit seven-dimensional transitive groups of local holomorphic transformations. The description splits into two cases corresponding to strictly pseudoconvex surfaces and surfaces with nondegenerate sign-indefinite Levi form.
Keywords: homogeneous manifold, normal form of equation, vector field, isotropy group, Levi form. 
@article{FAA_2002_36_2_a9,
     author = {A. V. Loboda},
     title = {Homogeneous {Nondegenerate} {Hypersurfaces} in $\mathbb{C}^3$ with {Two-Dimensional} {Isotropy} {Groups}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {80--83},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a9/}
}
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A. V. Loboda. Homogeneous Nondegenerate Hypersurfaces in $\mathbb{C}^3$ with Two-Dimensional Isotropy Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 80-83. http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a9/