  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.
