Metric Möbius geometry and a characterization of spheres

DOI10.1007/s00229-012-0555-0zbMath1270.51016arXiv1008.3250OpenAlexW1987794013MaRDI QIDQ1942238

Viktor Schroeder, Thomas Foertsch

Publication date: 18 March 2013

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.3250

zbMATH Keywords

Ptolemy metric spaceMöbius structureMöbius spaceMöbius equivalence

Mathematics Subject Classification ID

Distance geometry (51K99) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (7)

Ptolemy spaces with strong inversions ⋮ Möbius structures and timed causal spaces on the circle ⋮ Ptolemy circles and Ptolemy segments ⋮ Möbius characterization of hemispheres ⋮ Möbius characterization of the boundary at infinity of rank one symmetric spaces ⋮ Incidence axioms for the boundary at infinity of complex hyperbolic spaces ⋮ SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of the zz-distance for Möbius structures on the circle

Cites Work

• Hyperbolizing hyperspaces
• Hyperbolicity, CAT(\(-1\))-spaces and the Ptolemy inequality
• A geometric characterization of negatively curved locally symmetric spaces
• Conformal structure on the boundary and geodesic flow of a \(\text{CAT}(-1)\)-space
• Group actions on geodesic Ptolemy spaces
• Spaces with many affine functions
• PTOLEMAIC SPACES AND CAT(0)
• Nonpositive Curvature and the Ptolemy Inequality
• A Remark on M. M. Day's Characterization of Inner-Product Spaces and a Conjecture of L. M. Blumenthal

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