Abstract
We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
References
[1] S. Buyalo, V. Schroeder, Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces, arXiv:1012.1699, 2010. Search in Google Scholar
[2] S. Buyalo, V. Schroeder, Möbius characterization of the boundary at infinity of rank one symmetric spaces, Geometriae Dedicata, 172, (2014), no.1, 1-45. Search in Google Scholar
[3] S. Buyalo, V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, 2007, 209 pages. 10.4171/036Search in Google Scholar
[4] R. Chow, Groups quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757–1769. Search in Google Scholar
[5] T. Foertsch, V. Schroeder, Metric Möbius geometry and a characterization of spheres, Manuscripta Math. 140 (2013), no. 3-4, 613–620. Search in Google Scholar
[6] T. Foertsch, V. Schroeder, Hyperbolicity, CAT(−1)-spaces and Ptolemy inequality, Math. Ann. 350 (2011), no. 2, 339–356. Search in Google Scholar
[7] P. Hitzelberger, A. Lytchak, Spaces with many affine functions, Proc. Amer. Math. Soc. 135 (2007), no. 7, 2263–2271. Search in Google Scholar
[8] L. Kramer, Two-transitive Lie groups, J. reine angew. Math. 563 (2003), 83–113. Search in Google Scholar
[9] I. Mineyev, Metric conformal structures and hyperbolic dimension, Conform. Geom. Dyn. 11 (2007), 137–163 (electronic). 10.1090/S1088-4173-07-00165-8Search in Google Scholar
© 2015 Sergei Buyalo, Viktor Schroeder
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.