zbMATH — the first resource for mathematics

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.

53A30 Conformal differential geometry (MSC2010)
53B15 Other connections
53C29 Issues of holonomy in differential geometry
53C30 Differential geometry of homogeneous manifolds
Full Text: EMIS EuDML arXiv