New Randers metrics defined by the other Randers metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910547980582912 |
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| author | Fatahi, Azar Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| author_facet | Fatahi, Azar Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Randers metrics defined by the other Randers metrics Fatahi, Azar Hosseini, Masoumeh Moghaddam, Hamid Reza Salimi Differential Geometry 53C30, 53C60, 53C25, 22E60 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. |
| title | New Randers metrics defined by the other Randers metrics |
| topic | Differential Geometry 53C30, 53C60, 53C25, 22E60 |
| url | https://arxiv.org/abs/2407.21044 |