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

2007/10/12 by A. V. Isaev, Isaev, A. V.
Mathematics · #32C05 #32V40 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32C05 #msc:32V40

paper · pdf · doi:10.48550/arxiv.0710.2388

arxiv created 2007/10/12 · arxiv updated 2009/12/01

Abstract

We explicitly describe germs of strongly pseudoconvex non-spherical real-analytic hypersurfaces M at the origin in \CCⁿ⁺¹ for which the group of local CR-automorphisms preserving the origin has dimension d₀(M) equal to either n²-2n+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 \CC³ 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)≥ n²-2n+2.

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