On almost rational Finsler metrics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910506689757184 |
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| author | Taha, Ebtsam H. Tiwari, Bankteshwar |
| author_facet | Taha, Ebtsam H. Tiwari, Bankteshwar |
| contents | We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality of the associated geometric objects such as Cartan torsion, geodesic spray, Landsberg curvature, $S$-curvature, etc is investigated. We prove for a particular subset of AR-Finsler metrics that if $F$ has isotropic $S$-curvature, then its $S$-curvature identically vanishes. Further, if $F$ has isotropic mean Landsberg curvature, then it is weakly Landsberg. Also, if $F$ is an Einstein metric, then it is Ricci-flat. Moreover, we show that Randers metric can not be AR-Finsler metric. Finally, we provide some examples of AR-Finsler metrics and introduce a new Finsler metric which is called an extended $m$-th root metric. We show under what conditions an extended $m$-th root metric is AR-Finsler metric and study its generalized Kropina change. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_01764 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On almost rational Finsler metrics Taha, Ebtsam H. Tiwari, Bankteshwar Differential Geometry We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality of the associated geometric objects such as Cartan torsion, geodesic spray, Landsberg curvature, $S$-curvature, etc is investigated. We prove for a particular subset of AR-Finsler metrics that if $F$ has isotropic $S$-curvature, then its $S$-curvature identically vanishes. Further, if $F$ has isotropic mean Landsberg curvature, then it is weakly Landsberg. Also, if $F$ is an Einstein metric, then it is Ricci-flat. Moreover, we show that Randers metric can not be AR-Finsler metric. Finally, we provide some examples of AR-Finsler metrics and introduce a new Finsler metric which is called an extended $m$-th root metric. We show under what conditions an extended $m$-th root metric is AR-Finsler metric and study its generalized Kropina change. |
| title | On almost rational Finsler metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2101.01764 |