Non-positive curvature and the Ptolemy inequality

Thomas Foertsch; Alexander Lytchak; Viktor Schroeder

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arXiv · 0705.1042

Non-positive curvature and the Ptolemy inequality

Thomas Foertsch·Alexander Lytchak·Viktor Schroeder

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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.

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Thomas Foertsch, Alexander Lytchak, Viktor Schroeder. 2007-05-08. Non-positive curvature and the Ptolemy inequality. https://arxiv.org/abs/0705.1042

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