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Buckley, Stephen M., Falk, K. and Wraith, David (2009) Ptolemaic spaces and CAT (0). Glasgow Mathematical Journal, 51. pp. 301-314. ISSN 0017-0895
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Abstract
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 |
| Related URLs: | |
| URI: | https://mu.eprints-hosting.org/id/eprint/1570 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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