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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Ovidius University, Constanţa, Romania

    Wladimir G. Boskoff

  2. Department of Mathematics, California State University, Fullerton, CA, 92834-6850, USA

    Bogdan D. Suceavă

Authors
  1. Wladimir G. Boskoff
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  2. Bogdan D. Suceavă
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Correspondence to Wladimir G. Boskoff.

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Boskoff, W.G., Suceavă, B.D. Barbilian’s metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics. Czech Math J 58, 1059–1068 (2008). https://doi.org/10.1007/s10587-008-0068-x

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