Homogeneous strictly pseudoconvex hypersurfaces in C³ with two-dimensional isotropy groups

Strictly pseudoconvex non-spherical hypersurfaces in 3-dimensional complex space that are homogeneous with respect to local Lie groups of holomorphic transformations are studied. The?author proved earlier that a?Lie group Aut?M acting transitively on such a?manifold?M has dimension at most?7.A complete list of homogeneous surfaces such that Aut?M has dimension precisely?7 (and the corresponding isotropy subgroup has dimension precisely?2) is given. The?main tools used in the paper are local normal equations describing the manifolds under consideration.