Randers Metrics of Berwald type on 4-dimensional hypercomplex Lie groups

TL;DR

This paper investigates Randers metrics of Berwald type on 4-dimensional hypercomplex Lie groups, providing explicit formulas for flag curvature and constructing examples with non-negative and non-positive curvature.

Contribution

It introduces explicit formulas for flag curvature of Randers Berwald metrics on hypercomplex Lie groups and constructs specific examples with controlled curvature signs.

Findings

Constructed two 4D Berwald spaces with specified curvature signs

Derived explicit formulas for flag curvature in this setting

Identified conditions for non-negative and non-positive flag curvature

Abstract

In the present paper we study Randers metics of Berwald type on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. On these spaces, the Randers metrics arising from invariant hyper-Hermitian metrics are considered. Then we give explicit formulas for computing flag curvature of these metrics. By this study we construct two 4-dimensional Berwald spaces, one of them has non-negative flag curvature and the other one has non-positive flag curvature.