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...
Збережено в:
| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/6875 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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 |