Metric projections versus non-positive curvature

TL;DR

This paper introduces two metric properties based on projections to characterize non-positive curvature in various geometric spaces, including Alexandrov, Busemann NPC spaces, and Finsler-Minkowski spaces.

Contribution

It defines new metric properties via projections that precisely characterize non-positive curvature in diverse geodesic spaces and manifolds.

Findings

Characterization of non-positive curvature using metric projections

Validation of properties on Alexandrov and Busemann NPC spaces

Extension of results to Finsler-Minkowski spaces

Abstract

In this paper two metric properties on geodesic length spaces are introduced by means of the metric projection, studying their validity on Alexandrov and Busemann NPC spaces. In particular, we prove that both properties characterize the non-positivity of the sectional curvature on Riemannian manifolds. Further results are also established on reversible/non-reversible Finsler-Minkowski spaces.