MURAL - Maynooth University Research Archive Library



    Ptolemaic spaces and CAT (0)


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

    [img] Download (173kB)
    Official URL: http://journals.cambridge.org/action/displayIssue?...


    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...



    Add this article to your Mendeley library


    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
    URI:

    Repository Staff Only(login required)

    View Item Item control page

    Downloads

    Downloads per month over past year