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

Wladimir G. Boskoff; Bogdan D. Suceavă

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1059-1068
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Boskoff, Wladimir G., and Suceavă, Bogdan D.. "Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics." Czechoslovak Mathematical Journal 58.4 (2008): 1059-1068. <http://eudml.org/doc/37885>.

@article{Boskoff2008,
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.},
author = {Boskoff, Wladimir G., Suceavă, Bogdan D.},
journal = {Czechoslovak Mathematical Journal},
keywords = {\{Riemannian metrics; Finslerian metrics; Lagrangian metrics; Lagrange generalized metrics; Barbilian's metrization procedure; Apollonian metric\}; Riemannian metrics; Finslerian metrics; Lagrangian metrics; Lagrange generalized metrics; Barbilian's metrization procedure; Apollonian metric},
language = {eng},
number = {4},
pages = {1059-1068},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics},
url = {http://eudml.org/doc/37885},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Boskoff, Wladimir G.
AU - Suceavă, Bogdan D.
TI - Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1059
EP - 1068
AB - 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.
LA - eng
KW - {Riemannian metrics; Finslerian metrics; Lagrangian metrics; Lagrange generalized metrics; Barbilian's metrization procedure; Apollonian metric}; Riemannian metrics; Finslerian metrics; Lagrangian metrics; Lagrange generalized metrics; Barbilian's metrization procedure; Apollonian metric
UR - http://eudml.org/doc/37885
ER -

References

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