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Invariants of elliptic and hyperbolic CR-structures of codimension 2
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.Comment: 42 pages, see also
http://wwwmaths.anu.edu.au/research.reports/97mrr.htm
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