On Chern-Moser Normal Forms of Strongly Pseudoconvex Hypersurfaces with High-Dimensional Stability Group

We explicitly describe germs of strongly pseudoconvex non-spherical real-analytic hypersurfaces M at the origin in Cn+1 for which the group of local CR-automorphisms preserving the origin has dimension d0(M) equal to either n 2 − 2n + 1 with n ≥ 2, or n2 − 2n with n ≥ 3. The description is given in terms of equations defining hypersurfaces near the origin, written in the Chern-Moser normal form. These results are motivated by the classification of locally homogeneous Levi non-degenerate hypersurfaces in C3 with d0(M) = 1, 2 due to A. Loboda, and complement earlier joint work by V. Ezhov and the author for the case d0(M) ≥ n 2 − 2n + 2.