On Chern-Moser normal forms of strongly pseudoconvex hypersurfaces with high-dimensional stability group

摘要

We explicitly describe germs of strongly pseudoconvex nonspherical real-analytic hypersurfaces M at the origin in Cn+1 for which the group of local CR-automorphisms preserving the origin has dimension d(0)(M) equal to either n(2)-2n+1 with n >= 2 or n(2)-2n with n >= 3. The description is given in terms of equations defining hypersurfaces near the origin, which are written in the Chern-Moser normal form. These results are motivated by the classification of locally homogeneous Levi nondegenerate hypersurfaces in C-3 with d(0)(M) = 1, 2 due to A. Loboda, and they complement earlier joint work by V. Ezhov and the author for the case d(0)(M) >= n(2)-2n+2.