Noether Symmetries of the Area-Minimizing Lagrangian
It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1)-area enclosing a constant n-volume in a Euclidean space is so(n)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). Furthermore, if the space has one section of constant curvature of dimensi...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/532690 |
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| author | Adnan Aslam Asghar Qadir |
| author_facet | Adnan Aslam Asghar Qadir |
| author_sort | Adnan Aslam |
| collection | DOAJ |
| description | It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1)-area enclosing a constant n-volume in a Euclidean space is so(n)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n≥∑j=1knj+m (as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is ⊕j=1kso(nj+1)⊕(so(m)⊕sℝm). |
| format | Article |
| id | doaj-art-7c58f87e9bfd4e0f810d2fa977f7a270 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7c58f87e9bfd4e0f810d2fa977f7a2702025-02-03T01:33:03ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/532690532690Noether Symmetries of the Area-Minimizing LagrangianAdnan Aslam0Asghar Qadir1Center for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology (NUST), H-12, 44000 Islamabad, PakistanCenter for Advanced Mathematics and Physics (CAMP), National University of Sciences and Technology (NUST), H-12, 44000 Islamabad, PakistanIt is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an (n-1)-area enclosing a constant n-volume in a Euclidean space is so(n)⊕sℝn and in a space of constant curvature the Lie algebra is so(n). Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n≥∑j=1knj+m (as some of the sections may have no symmetry), then the Lie algebra of Noether symmetries is ⊕j=1kso(nj+1)⊕(so(m)⊕sℝm).http://dx.doi.org/10.1155/2012/532690 |
| spellingShingle | Adnan Aslam Asghar Qadir Noether Symmetries of the Area-Minimizing Lagrangian Journal of Applied Mathematics |
| title | Noether Symmetries of the Area-Minimizing Lagrangian |
| title_full | Noether Symmetries of the Area-Minimizing Lagrangian |
| title_fullStr | Noether Symmetries of the Area-Minimizing Lagrangian |
| title_full_unstemmed | Noether Symmetries of the Area-Minimizing Lagrangian |
| title_short | Noether Symmetries of the Area-Minimizing Lagrangian |
| title_sort | noether symmetries of the area minimizing lagrangian |
| url | http://dx.doi.org/10.1155/2012/532690 |
| work_keys_str_mv | AT adnanaslam noethersymmetriesoftheareaminimizinglagrangian AT asgharqadir noethersymmetriesoftheareaminimizinglagrangian |