Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle
In the present paper, a Riemannian metric on the tangent bundle, which is another generalization of Cheeger-Gromoll metric and Sasaki metric, is considered. This metric is known as Kaluza-Klein metric in literature which is completely determined by its action on vector fields of type X^{H} and Y^{V...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2022-12-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52990 |
| _version_ | 1797633583754510336 |
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| author | Haşim Çayir |
| author_facet | Haşim Çayir |
| author_sort | Haşim Çayir |
| collection | DOAJ |
| description |
In the present paper, a Riemannian metric on the tangent bundle, which is another generalization of Cheeger-Gromoll metric and Sasaki metric, is considered. This metric is known as Kaluza-Klein metric in literature which is completely determined by its action on vector fields of type X^{H} and Y^{V}. We obtain the covarient and Lie derivatives applied to the Kaluza-Klein metric with respect to the horizontal and vertical lifts of vector fields, respectively on tangent bundle TM.
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| first_indexed | 2024-03-11T11:55:56Z |
| format | Article |
| id | doaj.art-8a8dbdd47a694012ae1215a88b6edcd3 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:56Z |
| publishDate | 2022-12-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-8a8dbdd47a694012ae1215a88b6edcd32023-11-08T19:10:32ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882022-12-014110.5269/bspm.52990Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundleHaşim Çayir0Giresun University In the present paper, a Riemannian metric on the tangent bundle, which is another generalization of Cheeger-Gromoll metric and Sasaki metric, is considered. This metric is known as Kaluza-Klein metric in literature which is completely determined by its action on vector fields of type X^{H} and Y^{V}. We obtain the covarient and Lie derivatives applied to the Kaluza-Klein metric with respect to the horizontal and vertical lifts of vector fields, respectively on tangent bundle TM. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52990 |
| spellingShingle | Haşim Çayir Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle Boletim da Sociedade Paranaense de Matemática |
| title | Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle |
| title_full | Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle |
| title_fullStr | Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle |
| title_full_unstemmed | Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle |
| title_short | Some calculations on Kaluza-Klein metric with respect to lifts in tangent bundle |
| title_sort | some calculations on kaluza klein metric with respect to lifts in tangent bundle |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/52990 |
| work_keys_str_mv | AT hasimcayir somecalculationsonkaluzakleinmetricwithrespecttoliftsintangentbundle |