Displaying similar documents to “On a construction of the normal Cartan connections for CR-structures”

On left invariant CR structures on SU ( 2 )

Andreas Čap (2006)

Archivum Mathematicum

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There is a well known one–parameter family of left invariant CR structures on S U ( 2 ) ≅ S 3 . We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

Free CR distributions

Gerd Schmalz, Jan Slovák (2012)

Open Mathematics

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There are only some exceptional CR dimensions and codimensions 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 with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in ℂ n + n 2 for all n...

Homogeneous Cartan geometries

Matthias Hammerl (2007)

Archivum Mathematicum

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We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal automorphisms. The main result of this paper is that the above calculations are purely algorithmic. As an example of an homogeneous parabolic geometry we treat a conformal structure on the product of two spheres.