Moebius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces

2010/12/08 by Sergei Buyalo, Buyalo, Sergei, Viktor Schroeder +1 · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #math.DG #math.MG #msc:53C35

paper · pdf · doi:10.48550/arxiv.1012.1699

77 pages

arxiv created 2010/12/08 · arxiv updated 2010/12/09

Abstract

The paper initiates a systematic study of Moebius structures and Ptolemy spaces. We conjecture that every compact Ptolemy space with circles and many space inversions is Moebius equivalent to the boundary at infinity of a rank one symmetric space of noncompact type. We prove this conjecture for the class of complex hyperbolic spaces as our main result.

Cited by

• Complex cross--ratios and the Ptolemaean inequality
• Moebius characterization of the boundary at infinity of rank one symmetric spaces
• Ptolemy spaces with strong inversions

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• Hyperbolic Spaces and Ptolemy Moebius Structures
• Ptolemy spaces with strong inversions
• On the inverse problem of Moebius geometry on the circle
• Inverse problem for Moebius geometry on the circle