  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.

Differential Geometry