On the left invariant Randers and Matsumoto metrics of Berwald type on 3-dimensional Lie groups

TL;DR

This paper classifies all 3D Lie groups that support specific Randers and Matsumoto metrics of Berwald type and provides explicit formulas for their flag curvatures.

Contribution

It identifies all 3D Lie groups admitting these metrics and derives explicit flag curvature formulas, advancing understanding of geometric structures on Lie groups.

Findings

Complete classification of 3D Lie groups with these metrics

Explicit formulas for flag curvatures

Characterization of Berwald type metrics on Lie groups

Abstract

In this paper we identify all simply connected 3-dimensional real Lie groups which admit Randers or Matsumoto metrics of Berwald type with a certain underlying left invariant Riemannian metric. Then we give their flag curvatures formulas explicitly.