English

New Randers metrics defined by the other Randers metrics

Differential Geometry 2024-08-01 v1

Abstract

In this short article, using a left-invariant Randers metric FF, we define a new left-invariant Randers metric F~\tilde{F}. We show that FF is of Berwald (Douglas) type if and only if F~\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.

Keywords

Cite

@article{arxiv.2407.21044,
  title  = {New Randers metrics defined by the other Randers metrics},
  author = {Azar Fatahi and Masoumeh Hosseini and Hamid Reza Salimi Moghaddam},
  journal= {arXiv preprint arXiv:2407.21044},
  year   = {2024}
}