Lenka Zalabová (2006)
Archivum Mathematicum
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We consider symmetries on filtered manifolds and we study the -graded parabolic geometries in more details. We discuss the existence of symmetries on the homogeneous models and we conclude some simple observations on the general curved 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.
Florian Wisser (2006)
Archivum Mathematicum
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The Fefferman construction associates to a manifold carrying a CR–structure a conformal structure on a sphere bundle over the manifold. There are some analogs to this construction, with one giving a Lie contact structure, a refinement of the contact bundle on the bundle of rays in the cotangent bundle of a manifold with a conformal metric. Since these structures are parabolic geometries, these constructions can be dealt with in this setting.