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Möbius characterization of the boundary at infinity of rank one symmetric spaces


Buyalo, Sergei; Schroeder, Viktor (2013). Möbius characterization of the boundary at infinity of rank one symmetric spaces. Geometriae Dedicata, 172(1):1-45.

Abstract

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 is Möbius equivalent to the boundary at infinity of a rank one symmetric space.

Abstract

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 is Möbius equivalent to the boundary at infinity of a rank one symmetric space.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:August 2013
Deposited On:27 Dec 2013 13:20
Last Modified:05 Apr 2016 17:17
Publisher:Springer
ISSN:0046-5755
Publisher DOI:https://doi.org/10.1007/s10711-013-9906-6

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