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. 
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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/

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