1999/05/26 by Peter Ebenfelt, Ebenfelt, Peter
Mathematics · #32F25 #32F40 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #math.DG #msc:32F25 #msc:32F40
paper · pdf · doi:10.48550/arxiv.math/9905163
29 pages; AMS-TeX
arxiv created 1999/05/26 · openalex publication_date 1999/05/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider real hypersurfaces M in \Bbb C3 (or more generally, 5-dimensional CR manifolds of hypersurface type) at uniformly Levi degenerate points, i.e. Levi degenerate points such that the rank of the Levi form is constant in a neighborhood. We also require the hypersurface to satisfy a certain second order nondegeneracy condition (called 2-nondegeneracy) at the point. Our first result is the construction of a principal bundle P→ M with an absolute parallelism, uniquely determined by the CR structure on M, which reduces the question of whether two such CR manifolds M and M' are CR equivalent to the corresponding equivalence problem for the parallelized bundles P and P'. A basic example of a hypersurface of the type under consideration is the tube Γ_\bC over the light cone. Our second result is the characterization of Γ_\bC by vanishing curvature conditions in the spirit of the characterization of the unit sphere as the flat model for strongly pseudoconvex hypersurfaces in \bCn+1 in terms of the Cartan-Chern-Moser connection.