Complex cross--ratios and the Ptolemaean inequality

2012/07/21 by Ioannis D. Platis, Platis, Ioannis D.
Mathematics · #32V05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications #Metric Geometry (math.MG) #math.DG #math.MG #msc:32V05

paper · pdf · doi:10.48550/arxiv.1207.5114

6 pages

arxiv created 2012/07/21 · openalex publication_date 2012/07/21 · arxiv updated 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use Korányi--Reimann complex cross--ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of complex hyperbolic space and the first Heisenberg group.

Citations

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

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