On the local representation of synectic connections on Weil bundles
Synectic extensions of complete lifts of linear connections in tangent bundles were introduced by A. P. Shirokov in the seventies of the last century [1; 2]. He established that these connections are linear and are real realizations of linear connections on first-order tangent bundles endowed with...
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| Format: | Article |
| Language: | English |
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Immanuel Kant Baltic Federal University
2022-11-01
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| Series: | Дифференциальная геометрия многообразий фигур |
| Subjects: |
| _version_ | 1811318339641802752 |
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| author | A. Ya. Sultanov G.A. Sultanova |
| author_facet | A. Ya. Sultanov G.A. Sultanova |
| author_sort | A. Ya. Sultanov |
| collection | DOAJ |
| description | Synectic extensions of complete lifts of linear connections in tangent bundles were introduced by A. P. Shirokov in the seventies of the last century [1; 2]. He established that these connections are linear and are real realizations of linear connections on first-order tangent bundles endowed with a smooth structure over the algebra of dual numbers. He also proved the existence of a smooth structure on tangent bundles of arbitrary order on a smooth manifold M over the algebra of plural numbers. Studying holomorphic linear connections on over an algebra , A. P. Shirokov obtained real realizations of these connections, which he called Synectic extensions of a linear connection defined on M. A natural generalization of the algebra of plural numbers is the A. Weyl algebra, and a generalization of the tangent bundle is the A. Weyl bundle. It was shown in [3] that a synectic extension of linear connections defined on M a smooth manifold can also be constructed on A. Weyl bundles , where is the A. Weyl algebra. The geometry of these bundles has been studied by many authors — A. Morimoto, V. V. Shurygin and others. A detailed analysis of these works can be found in [3].
In this paper, we study synectic lifts of linear connections defined on A. Weyl bundles.
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| first_indexed | 2024-04-13T12:23:51Z |
| format | Article |
| id | doaj.art-f54161cf493443dc806aabb98a7b447a |
| institution | Directory Open Access Journal |
| issn | 0321-4796 2782-3229 |
| language | English |
| last_indexed | 2024-04-13T12:23:51Z |
| publishDate | 2022-11-01 |
| publisher | Immanuel Kant Baltic Federal University |
| record_format | Article |
| series | Дифференциальная геометрия многообразий фигур |
| spelling | doaj.art-f54161cf493443dc806aabb98a7b447a2022-12-22T02:47:05ZengImmanuel Kant Baltic Federal UniversityДифференциальная геометрия многообразий фигур0321-47962782-32292022-11-015311812610.5922/0321-4796-2022-53-11On the local representation of synectic connections on Weil bundlesA. Ya. Sultanov0G.A. Sultanova1Penza State UniversityFederal State-Owned Logistic Military Educational Institution named after General A.V. Khrulyov of the Ministry of Defence of the Russian FederationSynectic extensions of complete lifts of linear connections in tangent bundles were introduced by A. P. Shirokov in the seventies of the last century [1; 2]. He established that these connections are linear and are real realizations of linear connections on first-order tangent bundles endowed with a smooth structure over the algebra of dual numbers. He also proved the existence of a smooth structure on tangent bundles of arbitrary order on a smooth manifold M over the algebra of plural numbers. Studying holomorphic linear connections on over an algebra , A. P. Shirokov obtained real realizations of these connections, which he called Synectic extensions of a linear connection defined on M. A natural generalization of the algebra of plural numbers is the A. Weyl algebra, and a generalization of the tangent bundle is the A. Weyl bundle. It was shown in [3] that a synectic extension of linear connections defined on M a smooth manifold can also be constructed on A. Weyl bundles , where is the A. Weyl algebra. The geometry of these bundles has been studied by many authors — A. Morimoto, V. V. Shurygin and others. A detailed analysis of these works can be found in [3]. In this paper, we study synectic lifts of linear connections defined on A. Weyl bundles. tangent bundleweyl algebrasynectic connectioncurvature tensor fieldtorsion tensor field |
| spellingShingle | A. Ya. Sultanov G.A. Sultanova On the local representation of synectic connections on Weil bundles Дифференциальная геометрия многообразий фигур tangent bundle weyl algebra synectic connection curvature tensor field torsion tensor field |
| title | On the local representation of synectic connections on Weil bundles |
| title_full | On the local representation of synectic connections on Weil bundles |
| title_fullStr | On the local representation of synectic connections on Weil bundles |
| title_full_unstemmed | On the local representation of synectic connections on Weil bundles |
| title_short | On the local representation of synectic connections on Weil bundles |
| title_sort | on the local representation of synectic connections on weil bundles |
| topic | tangent bundle weyl algebra synectic connection curvature tensor field torsion tensor field |
| work_keys_str_mv | AT ayasultanov onthelocalrepresentationofsynecticconnectionsonweilbundles AT gasultanova onthelocalrepresentationofsynecticconnectionsonweilbundles |