The homogeneous geometries of real hyperbolic space

2011/11/24 by Marco Castrillon Lopez, Lopez, Marco Castrillon, P. M. Gadea +3
Mathematics · #53C30 (primary) #57S25 #58H15 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C30 #msc:57S25 #msc:58H15

paper · pdf · doi:10.48550/arxiv.1111.5723

13 pages

arxiv created 2011/11/24 · arxiv updated 2011/11/28

Abstract

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.

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