Abstract
We construct a complete list of nonspherical real hypersurfaces in \(\mathbb{C}^{\text{3}} \) 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.
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Loboda, A.V. Homogeneous Nondegenerate Hypersurfaces in ℂ3with Two-Dimensional Isotropy Groups. Functional Analysis and Its Applications 36, 151–153 (2002). https://doi.org/10.1023/A:1015678825587
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DOI: https://doi.org/10.1023/A:1015678825587