On two natural Riemannian metrics on a tube.
Labbi, M.-L. (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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Labbi, M.-L. (2007)
Balkan Journal of Geometry and its Applications (BJGA)
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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.