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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… (More)

- Andreaš Cap, Gerd Schmalz

We extend the results of [11] on embedded CR manifolds of CR dimension and codimension two to abstract partially integrable almost CR manifolds. We prove that points on such manifolds fall into three different classes, two of which (the hyperbolic and the elliptic points) always make up open sets. We prove that manifolds consisting entirely of hyperbolic… (More)

- Gerd Schmalz, Andrea Spiro
- 2008

In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codi-mension two, i.e. a pair (P, ω), consisting of a principal bundle π : P → M over M and of a Cartan connection form ω over P , satisfying the following property: the (local) CR transformations f : M → M are in… (More)

- Gerd Schmalz, Jan Slovák, Jan Slov´ak
- 2012

There are only some exceptional CR dimensions and codi-mensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n + 1, n)/P… (More)

- Gerd Schmalz, Jan Slov´ak
- 1999

The general theory of parabolic geometries is applied to the study of the normal Cartan connections for all hyperbolic and elliptic 6-dimensional CR-manifolds of codimension two. The geometric meaning of the individual components of the torsion is explained and the chains of dimensions one and two are discussed. There have been many attempts to use some… (More)

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