On mean Cartan torsion of Finsler metrics
UDC 514.7 We prove  that Finsler manifolds with unbounded mean Cartan torsion cannot be isometrically imbedded into any Minkowski space.  We also study the generalized Randers metrics obtained by the Rizza structure and show that any generalized Randers metric...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6875 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 514.7
We prove  that Finsler manifolds with unbounded mean Cartan torsion cannot be isometrically imbedded into any Minkowski space.  We also study the generalized Randers metrics obtained by the Rizza structure and show that any generalized Randers metric has an unbounded mean Cartan torsion. Then  generalized Randers metrics   cannot be isometrically imbedded into any Minkowski space. Further, we prove that every generalized Randers metric is quasi-C-reducible.  Finally, we show that every generalized Randers metric on 2-dimensional  Finsler manifold has a vanishing mean Cartan torsion. |
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| DOI: | 10.37863/umzh.v75i3.6875 |