Completeness and incompleteness of the Binet-Legendre Metric
Vladimir S. Matveev, Marc Troyanov
TL;DR
This paper investigates conditions under which the Binet-Legendre metric is complete in Finsler geometry, with specific discussion on Funk and Hilbert metrics within convex domains.
Contribution
It provides new conditions for the completeness of the Binet-Legendre metric and analyzes specific cases like Funk and Hilbert metrics.
Findings
Conditions for completeness of the Binet-Legendre metric are established.
Analysis of Funk and Hilbert metrics in convex domains.
Insights into Finsler geometry completeness criteria.
Abstract
The goal of this short paper is to give condition for the completeness of the Binet-Legendre metric in Finsler geometry. The case of the Funk and Hilbert metrics in a convex domain are discussed.
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