New Randers metrics defined by the other Randers metrics

TL;DR

This paper introduces a new class of Randers metrics derived from existing ones on Lie groups, establishing their properties and relations, especially regarding Berwald and Douglas types, with applications to specific Lie groups.

Contribution

It defines a new Randers metric based on a given one and explores its geometric properties, including curvature and relations to the original metric, which is a novel approach.

Findings

F is of Berwald (Douglas) type iff ilde{F} is of the same type

Relations between flag curvatures of F and ilde{F} are established

Applications to Heisenberg and almost Abelian Lie groups demonstrate the theory

Abstract

In this short article, using a left-invariant Randers metric $F$, we define a new left-invariant Randers metric $\tilde{F}$. We show that $F$ is of Berwald (Douglas) type if and only if $\tilde{F}$ is of Berwald (Douglas) type. In the case of Berwaldian metrics, we give the relation between their flag curvatures. Also, we have studied the relations between their base Riemannian metrics. Finally, as examples, the results are studied in the Heisenberg group and almost Abelian Lie groups.