Homogeneous Cartan geometries

Matthias Hammerl

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.