Geodesic
Homogeneous Cartan geometries
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 431-442

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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.
Classification : 53A30, 53B15, 53C29, 53C30, 53Cxx
Keywords: Cartan geometry; homogeneous space; infinitesimal automorphism; holonomy; conformal geometry 
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     author = {Hammerl, Matthias},
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Hammerl, Matthias. Homogeneous Cartan geometries. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 431-442. http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a7/