Some Berwald Spaces of Non-positive flag Curvature

TL;DR

This paper constructs specific examples of Berwald spaces with non-positive flag curvature using invariant metrics on Lie groups, including geodesically complete locally Minkowskian spaces with zero flag curvature.

Contribution

It introduces new complete non-Riemannian Berwald spaces and locally Minkowskian spaces with specific curvature properties on 3D Lie groups.

Findings

Construction of complete non-Riemannian Berwald spaces of non-positive flag curvature

Families of geodesically complete locally Minkowskian spaces with zero flag curvature

Use of invariant metrics on Lie groups for space construction

Abstract

In this paper by using left invariant Riemannian metrics on some 3-dimensional Lie groups we construct some complete non-Riemannian Berwald spaces of non-positive flag curvature and several families of geodesically complete locally Minkowskian spaces of zero constant flag curvature.