More on Riemann metrics in \(\mathbb R^2\) for which the lines are the shortest paths
type: Item
instance of: scholarly article
title: More on Riemann metrics in \(\mathbb R^2\) for which the lines are the shortest paths
zbMATH Open document ID: 0955.53026
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1999-06-16T00:00:00Z
review text: The author studies the parametric version of Hilbert's fourth problem in the context of Riemann metrics: Describing all Riemann metrics on the Euclidean plane \(\mathbb R^2\) for which the usual lines are the geodesics (called Hilbert metrics). A criterion is derived giving necessary and sufficient conditions for the geodesics of a Riemann metric defined on \(\mathbb R^2\) to be the usual straight lines. As an application of this criterion the author finds out the unique Hilbert metric in a class of isotropic Riemann metrics with isotropic orientation function.
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 1193060
zbMATH Keywords: Hilbert's fourth problem
zbMATH Keywords: geodesics
zbMATH Keywords: Hilbert metric
zbMATH Keywords: isotropic Riemann metrics
author: Viktor Ohanyan
reviewed by: Nabil L. Youssef
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1193060