1998/04/09 by V. V. Ezhov, Vladimir Ezhov, A. V. Isaev +6
Mathematics · #32C05 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32C05
paper · pdf · doi:10.48550/arxiv.math/9804053
42 pages, see also http://wwwmaths.anu.edu.au/research.reports/97mrr.html
arxiv created 1998/04/09 · openalex publication_date 1998/04/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2 to parallelisms thus solving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequence of two principal bundles over the manifold, takes values in the Lie algebra of infinitesimal automorphisms of the quadric corresponding to the Levi form of the manifold, and behaves ``almost'' like a Cartan connection. The construction is explicit and allows us to study the properties of the parallelism as well as those of its curvature form. It also leads to a natural class of ``semi-flat'' manifolds for which the two bundles reduce to a single one and the parallelism turns into a true Cartan connection. In addition, for real-analytic manifolds we describe certain local normal forms that do not require passing to bundles, but in many ways agree with the structure of the parallelism.