Completeness and incompleteness of the Binet-Legendre Metric

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.

17 pages, 3 figures

References in corpus (2)

• On the Hilbert Geometry of Convex Polytopes
• Survey on Affine Spheres

Cited by in corpus (3)

• The Myers-Steenrod theorem for Finsler manifolds of low regularity
• If a Minkowski billiard is projective, it is the standard billiard
• $p$-Laplacian first eigenvalues controls on Finsler manifolds