Homogeneous Real Hypersurfaces in $\mathbb C^3$ with Two-Dimensional Isotropy Groups

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.