On normal equations of affinely homogeneous convex surfaces of the space \(\mathbb R^3\) (Q1599419)

The authors classify all strictly convex surfaces in \(\mathbb{R}^3\) which are homogeneous with respect to the full affine group. (For hyperbolic surfaces this was performed by the second author in Mat. Zametki 65, 793-797 (1999; Zbl 0976.53012). They determine the fourth order coefficients of a certain normal form. Another normal form was used by \textit{M. Eastwood} and \textit{V. Ezhov} [Geom. Dedicata 77, 11-69 (1999; Zbl 0999.53008)] for the classification of all homogeneous surfaces. \textit{B. Doubrov}, \textit{B. Komrakov} and \textit{M. Rabinovich} [Homogeneous surfaces in the three-dimensional affine geometry, in: F. Dillen et al. eds., Geometry and topology of submanifolds VIII, World Scientific, Singapore, 168-178 (1996; Zbl 0934.53007)] found this classification by studying the symmetry algebras and their subalgebras. A comparison of these methods and results can be found in the paper of Eastwood and Ezhov.