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 |
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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| _version_ | 1860512544291028992 |
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| author | Nezhad, A. Dehghan Beizavi, S. Nezhad, A. Dehghan Beizavi, S. |
| author_facet | Nezhad, A. Dehghan Beizavi, S. Nezhad, A. Dehghan Beizavi, S. |
| author_sort | Nezhad, A. Dehghan |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-04-15T15:10:31Z |
| description | 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. |
| doi_str_mv | 10.37863/umzh.v75i3.6875 |
| first_indexed | 2026-03-24T03:30:28Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6875 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:30:28Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-68752023-04-15T15:10:31Z On mean Cartan torsion of Finsler metrics On mean Cartan torsion of Finsler metrics Nezhad, A. Dehghan Beizavi, S. Nezhad, A. Dehghan Beizavi, S. Cartan torsion generalized Randers metric generalized $(a, b, J)$-metrics. 53B40 53C60 32Q60 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. УДК 514.7 Про картанове кручення метрик Фінслера Доведено, що фінслерові многовиди з необмеженим середнім крученням Kартана неможливо ізометрично вкласти в будь-який простір Мінковського.  Крім того, вивчаються узагальнені метрики Рандерса, отримані за структурою Ріцца, і показано, що будь-яка узагальнена метрика Рандерса має необмежене середнє картанове кручення.  Тоді узагальнені метрики Рандерса неможливо ізометрично вкласти в будь-який простір Мінковського.  Також доведено, що будь-яка узагальнена метрика Рандерса є квазі-C-звідною.  Насамкінець показано, що будь-яка узагальнена метрика Рандерса на 2-вимірному многовиді Фінслера має  середнє картанове кручення, що зникає.  Institute of Mathematics, NAS of Ukraine 2023-04-11 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6875 10.37863/umzh.v75i3.6875 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 3 (2023); 337 - 350 Український математичний журнал; Том 75 № 3 (2023); 337 - 350 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6875/9789 Copyright (c) 2023 Akbar Dehghan Nezhad, Sareh Beizavi |
| spellingShingle | Nezhad, A. Dehghan Beizavi, S. Nezhad, A. Dehghan Beizavi, S. On mean Cartan torsion of Finsler metrics |
| title | On mean Cartan torsion of Finsler metrics |
| title_alt | On mean Cartan torsion of Finsler metrics |
| title_full | On mean Cartan torsion of Finsler metrics |
| title_fullStr | On mean Cartan torsion of Finsler metrics |
| title_full_unstemmed | On mean Cartan torsion of Finsler metrics |
| title_short | On mean Cartan torsion of Finsler metrics |
| title_sort | on mean cartan torsion of finsler metrics |
| topic_facet | Cartan torsion generalized Randers metric generalized $(a b J)$-metrics. 53B40 53C60 32Q60 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6875 |
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