# Non-Berwaldian Randers metrics of Douglas type on four-dimensional hypercomplex Lie groups

## TL;DR

This paper classifies specific non-Berwaldian Randers metrics of Douglas type on four-dimensional hypercomplex Lie groups, providing formulas for flag curvature and comparing it with sectional curvature.

## Contribution

It presents a complete classification of non-Berwaldian Randers metrics of Douglas type on four-dimensional hypercomplex Lie groups and analyzes their curvature properties.

## Key findings

- Flag curvature formulas are derived.
- In some directions, flag curvature and sectional curvature share the same sign.
- Classification of these metrics is achieved.

## Abstract

In this paper we classify all non-Berwaldian Randers metrics of Douglas type arising from invariant hyper-Hermitian metrics on simply connected four-dimensional real Lie groups. Also, the formulas of the flag curvature are given and it is shown that, in some directions, the flag curvature of the Randers metrics and the sectional curvature of the hyper-Hermitian metrics have the same sign.