Non-positive curvature and the Ptolemy inequality
Metric Geometry
2007-05-23 v1
Abstract
We provide examples of non-locally compact geodesic Ptolemy metric spaces which are not uniquely geodesic. On the other hand, we show that locally compact, geodesic Ptolemy metric spaces are uniquely geodesic. Moreover, we prove that a metric space is CAT(0) if and only if it is Busemann convex and Ptolemy.
Keywords
Cite
@article{arxiv.0705.1042,
title = {Non-positive curvature and the Ptolemy inequality},
author = {Thomas Foertsch and Alexander Lytchak and Viktor Schroeder},
journal= {arXiv preprint arXiv:0705.1042},
year = {2007}
}
Comments
11 pages, 2 figures