The Ptolemaean inequality in the closure of complexhyperbolic planes

DOI10.3906/mat-1604-6zbMath1424.53074arXiv1604.00473OpenAlexW2963962309MaRDI QIDQ4633351

Nilgün Sönmez, Ioannis D. Platis

Publication date: 2 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.00473

zbMATH Keywords

complex hyperbolic planeCygan metricPtolemaean inequalityPtolemaeus' theorem

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Metric geometry (51F99) Sub-Riemannian geometry (53C17)

Cites Work

• Incidence axioms for the boundary at infinity of complex hyperbolic spaces
• Hyperbolicity, CAT(\(-1\))-spaces and the Ptolemy inequality
• Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1
• Möbius rigidity of invariant metrics in boundaries of symmetric spaces of rank-1
• The Ptolemaic inequality in Hilbert geometries
• PTOLEMAIC SPACES AND CAT(0)
• Erratum to: Nonpositive Curvature and the Ptolemy Inequality
• A Remark on M. M. Day's Characterization of Inner-Product Spaces and a Conjecture of L. M. Blumenthal
• Unnamed Item

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