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.
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Acknowledgments
The author was partially supported by the International Research Training Group 1133 “Geometry and Analysis of Symmetries”, the Sonderforschungsbereich/Transregio 45 “Periods, moduli spaces and arithmetic of algebraic varieties”, and the Max-Planck-Institut für Mathematik in Bonn.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Pohl, A.D. Ford fundamental domains in symmetric spaces of rank one. Geom Dedicata 147, 219–276 (2010). https://doi.org/10.1007/s10711-009-9453-3
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DOI: https://doi.org/10.1007/s10711-009-9453-3
Keywords
- Ford fundamental domains
- Isometric fundamental regions
- Rank one symmetric spaces
- Isometric spheres
- Cygan metric