Distances Induced by Barbilian's Metrization Procedure

Details Distances Induced by Barbilian's Metrization Procedure Distances Induced by Barbilian's Metrization Procedure

2006-06-24

arxiv.org/abs/math/0606608v1

Mathematics

Differential Geometry

To appear in Houston J. Math

Scientific paper

Several authors have pointed out the connection between Barbilian's metric introduced in 1934 and the recent study of Apollonian metrics. We provide examples of various distances that can be obtained by Barbilian's metrization procedure and we discuss the relation between this metrization procedure and important Riemannian and generalized Lagrangian metrics. Then we prove an extension of Barbilian's metrization procedure.

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