On Holomorphic Homogeneity of Real Hypersurfaces of General Position in $\mathbb C^3$

Holomorphically homogeneous strictly pseudoconvex real hypersurfaces of three-dimensional complex spaces are studied within the coefficient approach. It is shown that the family of surfaces for which a fourth-degree polynomial in the Moser normal equation has a general form is described by at most 13 real parameters. Examples related to the normal equations of tubes over affine homogeneous bases are given which confirm the results of accompanying computer calculations.