Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection
In this study, we present a problem that consists in flattening the curvature associated with an affine connection on ℝ2. This problem involves distributions and symmetric affine connections defined on a differential manifold M. For rank 1 constant distributions, we characterize the existence of sol...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1528246 |
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| _version_ | 1849309065710141440 |
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| author | Esperanza Cuellar Ana C. Silva David A. Lizárraga |
| author_facet | Esperanza Cuellar Ana C. Silva David A. Lizárraga |
| author_sort | Esperanza Cuellar |
| collection | DOAJ |
| description | In this study, we present a problem that consists in flattening the curvature associated with an affine connection on ℝ2. This problem involves distributions and symmetric affine connections defined on a differential manifold M. For rank 1 constant distributions, we characterize the existence of solutions and get sufficient conditions to solve the problem. The general statement of the problem and some illustrative examples are given. |
| format | Article |
| id | doaj-art-065ee03edede4638ac25342cc3143027 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-065ee03edede4638ac25342cc31430272025-08-20T03:54:16ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1528246Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine ConnectionEsperanza Cuellar0Ana C. Silva1David A. Lizárraga2División de Control y Sistemas DinámicosDivisión de Control y Sistemas DinámicosDivisión de Control y Sistemas DinámicosIn this study, we present a problem that consists in flattening the curvature associated with an affine connection on ℝ2. This problem involves distributions and symmetric affine connections defined on a differential manifold M. For rank 1 constant distributions, we characterize the existence of solutions and get sufficient conditions to solve the problem. The general statement of the problem and some illustrative examples are given.http://dx.doi.org/10.1155/2022/1528246 |
| spellingShingle | Esperanza Cuellar Ana C. Silva David A. Lizárraga Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection Journal of Mathematics |
| title | Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection |
| title_full | Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection |
| title_fullStr | Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection |
| title_full_unstemmed | Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection |
| title_short | Conditions to Flatten the Curvature Tensor Associated with a Symmetric Affine Connection |
| title_sort | conditions to flatten the curvature tensor associated with a symmetric affine connection |
| url | http://dx.doi.org/10.1155/2022/1528246 |
| work_keys_str_mv | AT esperanzacuellar conditionstoflattenthecurvaturetensorassociatedwithasymmetricaffineconnection AT anacsilva conditionstoflattenthecurvaturetensorassociatedwithasymmetricaffineconnection AT davidalizarraga conditionstoflattenthecurvaturetensorassociatedwithasymmetricaffineconnection |