Hilbert metrics and Minkowski norms
2005 (English)In: Journal of Geometry, ISSN 0047-2468, E-ISSN 1420-8997, Vol. 83, no 1-2, 22-31 p.Article in journal (Refereed) Published
It is shown that the Hilbert geometry (D,h D ) associated to a bounded convex domain D ⊂ double struck E signn is isometric to a normed vector space (V,∥ ̇ ∥) if and only if D is an open n-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a Hilbert geometry converges to a point of the boundary.
Place, publisher, year, edition, pages
2005. Vol. 83, no 1-2, 22-31 p.
Asymptotic geometry, Hilbert metric
IdentifiersURN: urn:nbn:se:kth:diva-156520DOI: 10.1007/s00022-005-0005-1ScopusID: 2-s2.0-29644433138OAI: oai:DiVA.org:kth-156520DiVA: diva2:767259
QC 201412012014-12-012014-11-282015-10-16Bibliographically approved