Metric Möbius geometry and a characterization of spheres

Abstract

We obtain a Möbius characterization of the n-dimensional spheres S n endowed with the chordal metric d 0. We show that every compact extended Ptolemy metric space with the property that every three points are contained in a circle is Möbius equivalent to (S n, d 0) for some n ≥ 1.

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Correspondence to Viktor Schroeder.

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Foertsch, T., Schroeder, V. Metric Möbius geometry and a characterization of spheres. manuscripta math. 140, 613–620 (2013). https://doi.org/10.1007/s00229-012-0555-0

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Mathematics Subject Classification

  • 51K99