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Homogeneous Cartan geometries. (English) Zbl 1199.53021
Summary: 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.

MSC:
53A30 Conformal differential geometry (MSC2010)
53B15 Other connections
53C29 Issues of holonomy in differential geometry
53C30 Differential geometry of homogeneous manifolds
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