Publication: Möbius characterization of the boundary at infinity of rank one symmetric spaces
Möbius characterization of the boundary at infinity of rank one symmetric spaces
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Buyalo, S., & Schroeder, V. (2013). Möbius characterization of the boundary at infinity of rank one symmetric spaces. Geometriae Dedicata, 172(1), 1–45. https://doi.org/10.1007/s10711-013-9906-6
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Möbius structure (on a set X ) is a class of metrics having the same cross-ratios. A Möbius structure is Ptolemaic if it is invariant under inversion operations. The boundary at infinity of a CAT(−1) space is in a natural way a Möbius space, which is Ptolemaic. We give a free of classification proof of the following result that characterizes the rank one symmetric spaces of noncompact type purely in terms of their Möbius geometry: Let X be a compact Ptolemy space which contains a Ptolemy circle and allows many space inversions. Then X
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- Buyalo, Sergei
- Schroeder, Viktor
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Buyalo, S., & Schroeder, V. (2013). Möbius characterization of the boundary at infinity of rank one symmetric spaces. Geometriae Dedicata, 172(1), 1–45. https://doi.org/10.1007/s10711-013-9906-6
