Group actions on geodesic Ptolemy spaces
نویسندگان
چکیده
In this paper we study geodesic Ptolemy metric spaces X which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We show that X is equivariantly rough isometric to a Euclidean space.
منابع مشابه
ar X iv : 0 70 5 . 10 42 v 1 [ m at h . M G ] 8 M ay 2 00 7 NON - POSITIVE CURVATURE AND THE PTOLEMY INEQUALITY
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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