On GDW-Randers metrics on tangent Lie groups
Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we charac...
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| Format: | Article |
| Language: | English |
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Amirkabir University of Technology
2021-02-01
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| Series: | AUT Journal of Mathematics and Computing |
| Subjects: | |
| Online Access: | https://ajmc.aut.ac.ir/article_4160_a7fc31b063685455f8fddb080aaffa75.pdf |
| _version_ | 1797307117723451392 |
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| author | Mona Atashafrouz Behzad Najafi Akbar Tayebi |
| author_facet | Mona Atashafrouz Behzad Najafi Akbar Tayebi |
| author_sort | Mona Atashafrouz |
| collection | DOAJ |
| description | Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics. |
| first_indexed | 2024-03-08T00:51:42Z |
| format | Article |
| id | doaj.art-2b041fc7e6504c69915f831de611861c |
| institution | Directory Open Access Journal |
| issn | 2783-2449 2783-2287 |
| language | English |
| last_indexed | 2024-03-08T00:51:42Z |
| publishDate | 2021-02-01 |
| publisher | Amirkabir University of Technology |
| record_format | Article |
| series | AUT Journal of Mathematics and Computing |
| spelling | doaj.art-2b041fc7e6504c69915f831de611861c2024-02-14T19:37:14ZengAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492783-22872021-02-0121273610.22060/ajmc.2020.18572.10384160On GDW-Randers metrics on tangent Lie groupsMona Atashafrouz0Behzad Najafi1Akbar Tayebi2Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranDepartment of Mathematics, Faculty of Science, University of Qom, Qom, IranLet $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics.https://ajmc.aut.ac.ir/article_4160_a7fc31b063685455f8fddb080aaffa75.pdfleft-invariant metricdouglas metricgeneralized douglas-weyl metricsranders metric |
| spellingShingle | Mona Atashafrouz Behzad Najafi Akbar Tayebi On GDW-Randers metrics on tangent Lie groups AUT Journal of Mathematics and Computing left-invariant metric douglas metric generalized douglas-weyl metrics randers metric |
| title | On GDW-Randers metrics on tangent Lie groups |
| title_full | On GDW-Randers metrics on tangent Lie groups |
| title_fullStr | On GDW-Randers metrics on tangent Lie groups |
| title_full_unstemmed | On GDW-Randers metrics on tangent Lie groups |
| title_short | On GDW-Randers metrics on tangent Lie groups |
| title_sort | on gdw randers metrics on tangent lie groups |
| topic | left-invariant metric douglas metric generalized douglas-weyl metrics randers metric |
| url | https://ajmc.aut.ac.ir/article_4160_a7fc31b063685455f8fddb080aaffa75.pdf |
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