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Homogeneous Cartan geometries

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Matthias Hammerl
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** Address.**
Institut fuer Mathematik, Universitaet Wien

Nordbergstrasse 15, A-1090 Wien, Austria

** E-mail:**
matthias.hammerl@univie.ac.at

**Abstract.**
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.

**AMSclassification. ** 53A30, 53B15, 53C29, 53C30.

**Keywords. ** Cartan geometry, homogeneous space, infinitesimal automorphism, holonomy, conformal geometry.