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

A. V. Isaev

Vol. 235 (2008), No. 2, 235–244

DOI: 10.2140/pjm.2008.235.235

Abstract

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 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, which are written in the Chern–Moser normal form. These results are motivated by the classification of locally homogeneous Levi nondegenerate hypersurfaces in ℂ³ with d₀(M) = 1,2 due to A. Loboda, and they complement earlier joint work by V. Ezhov and the author for the case d₀(M) ≥ n² − 2n + 2.

Keywords

Chern–Moser normal forms, strongly pseudoconvex hypersurfaces, local CR-automorphisms

Mathematical Subject Classification 2000

Primary: 32V40

Secondary: 32C05

Milestones

Received: 7 October 2007

Revised: 24 January 2008

Accepted: 25 January 2008

Published: 1 April 2008