Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces

Sergei Buyalo; Viktor Schroeder

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 244-277, electronic only
  • ISSN: 2299-3274

Abstract

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We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

How to cite

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Sergei Buyalo, and Viktor Schroeder. "Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 244-277, electronic only. <http://eudml.org/doc/271752>.

@article{SergeiBuyalo2015,
abstract = {We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.},
author = {Sergei Buyalo, Viktor Schroeder},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {complex hyperbolic spaces; Ptolemy spaces; incidence axioms},
language = {eng},
number = {1},
pages = {244-277, electronic only},
title = {Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces},
url = {http://eudml.org/doc/271752},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Sergei Buyalo
AU - Viktor Schroeder
TI - Incidence Axioms for the Boundary at Infinity of Complex Hyperbolic Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 244
EP - 277, electronic only
AB - We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
LA - eng
KW - complex hyperbolic spaces; Ptolemy spaces; incidence axioms
UR - http://eudml.org/doc/271752
ER -

References

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  1. [1] S. Buyalo, V. Schroeder, Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces, arXiv:1012.1699, 2010.  
  2. [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. [WoS] Zbl06357997
  3. [3] S. Buyalo, V. Schroeder, Elements of asymptotic geometry, EMS Monographs in Mathematics, 2007, 209 pages.  Zbl1125.53036
  4. [4] R. Chow, Groups quasi-isometric to complex hyperbolic space. Trans. Amer. Math. Soc. 348 (1996), no. 5, 1757–1769.  Zbl0867.20033
  5. [5] T. Foertsch, V. Schroeder, Metric Möbius geometry and a characterization of spheres, Manuscripta Math. 140 (2013), no. 3-4, 613–620. [WoS] Zbl1270.51016
  6. [6] T. Foertsch, V. Schroeder, Hyperbolicity, CAT(−1)-spaces and Ptolemy inequality, Math. Ann. 350 (2011), no. 2, 339–356. [WoS] Zbl1219.53042
  7. [7] P. Hitzelberger, A. Lytchak, Spaces with many affine functions, Proc. Amer. Math. Soc. 135 (2007), no. 7, 2263–2271.  Zbl1128.53021
  8. [8] L. Kramer, Two-transitive Lie groups, J. reine angew. Math. 563 (2003), 83–113.  Zbl1044.22014
  9. [9] I. Mineyev, Metric conformal structures and hyperbolic dimension, Conform. Geom. Dyn. 11 (2007), 137–163 (electronic).  Zbl1165.20035

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