Ptolemaic spaces and CAT (0)

Buckley, S.M. and Falk, K. and Wraith, D.J. (2009) Ptolemaic spaces and CAT (0). Glasgow Mathematical Journal, 51. pp. 301-314. ISSN 0017-0895

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We consider Ptolemy’s inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0). Ptolemy’s inequality is closely related to inversions of metric spaces. We exploit this link to establish a new characterization of Euclidean space amongst all Riemannian manifolds.

Item Type: Article
Keywords: Ptolemaic spaces; CAT (0);
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 1570
Identification Number: 368937A635E648929124450838E73E03
Depositing User: Prof. Stephen Buckley
Date Deposited: 07 Oct 2009 12:02
Journal or Publication Title: Glasgow Mathematical Journal
Publisher: Cambridge University Press
Refereed: Yes

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