Ford fundamental domains in symmetric spaces of rank one

2009/08/28 by Anke D. Pohl, Pohl, Anke D.
Mathematics · #22E40 #52C22 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E40 #msc:52C22 #msc:53C35

paper · pdf · doi:10.48550/arxiv.0908.4203

54 pages; typos corrected

arxiv created 2009/12/14 · arxiv updated 2010/01/07

Abstract

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.

Related

• Rigidity of compact rank one symmetric spaces
• Existence of non-isotropic conjugate points on rank one normal homogeneous spaces
• Groups quasi-isometric to symmetric spaces
• A fundamental domain of Ford type for some subgroups of the orthogonal group
• A fundamental domain of Ford type for SO(3,Z[i])\backslash SO(3,C)/SO(3), and for SO(2,1)_Z\backslash SO(2,1)/SO(2)