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arXiv · 2407.21044

New Randers metrics defined by the other Randers metrics

Azar Fatahi·Masoumeh Hosseini·Hamid Reza Salimi Moghaddam
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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.

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Azar Fatahi, Masoumeh Hosseini, Hamid Reza Salimi Moghaddam. 2024-07-22. New Randers metrics defined by the other Randers metrics. https://arxiv.org/abs/2407.21044

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