The homogeneous geometries of real hyperbolic space

Preprint number: CP3-Origins-2011-42 and DIAS-2011-37
Authors: Marco Castrillón López (Universidad Complutense de Madrid), Pedro Martínez Gadea (CSIC), and Andrew Swann (CP3-Origins & Aarhus University)
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We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.