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Czechoslovak Mathematical Journal

, Volume 58, Issue 4, pp 1059–1068 | Cite as

Barbilian’s metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

  • Wladimir G. Boskoff
  • Bogdan D. Suceavă
Article

Abstract

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian’s metrization procedure can be relaxed. Then, we prove that Barbilian’s metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Keywords

Riemannian metrics Finslerian metrics Lagrangian metrics Lagrange generalized metrics Barbilian’s metrization procedure Apollonian metric 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceOvidius UniversityConstanţaRomania
  2. 2.Department of MathematicsCalifornia State UniversityFullertonUSA

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