arXiv subjects

Bogdan D. Suceava

Publications and source records attributed to Bogdan D. Suceava.

2 recordsLinked to original sources

arXiv2006

The History of Barbilian's Metrization Procedure

Barbilian spaces are metric spaces with a metric induced by a special procedure of metrization which is inspired by the study of the models of non-Euclidean geometry. In the present material we discuss the history of Barbilian spaces and the evolution of the theory. We point out that some of the current references to the work done in Barbilian spaces refer to Barbilian's contribution from 1934, while his construction has been largely extended in four works published in Romanian in 1959-1962.

math.HO↗

arXiv2006

Distances Induced by Barbilian's Metrization Procedure

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.

math.DG↗