INVARIANTS OF ELLIPTIC AND HYPERBOLIC CR-STRUCTURES OF CODIMENSION 2статья
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Дата последнего поиска статьи во внешних источниках: 16 июня 2023 г.
Аннотация: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.