Solving Local Equivalence Problems with the Equivariant Moving Frame Method
Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications...
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| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149233 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Solving Local Equivalence Problems with the Equivariant Moving Frame Method / F. Valiquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 42 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149233 |
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irk-123456789-1492332019-02-20T01:23:38Z Solving Local Equivalence Problems with the Equivariant Moving Frame Method Valiquette, F. Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications and assumptions, the equivariant moving frame constructions extend to submanifold jets where the pseudo-group does not act freely at any order. Once this is done, we review the solution to the local equivalence problem of submanifolds within the equivariant moving frame framework. This offers an alternative approach to Cartan's equivalence method based on the theory of G-structures. 2013 Article Solving Local Equivalence Problems with the Equivariant Moving Frame Method / F. Valiquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 42 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A55; 58A15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.029 http://dspace.nbuv.gov.ua/handle/123456789/149233 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Given a Lie pseudo-group action, an equivariant moving frame exists in the neighborhood of a submanifold jet provided the action is free and regular. For local equivalence problems the freeness requirement cannot always be satisfied and in this paper we show that, with the appropriate modifications and assumptions, the equivariant moving frame constructions extend to submanifold jets where the pseudo-group does not act freely at any order. Once this is done, we review the solution to the local equivalence problem of submanifolds within the equivariant moving frame framework. This offers an alternative approach to Cartan's equivalence method based on the theory of G-structures. |
| format |
Article |
| author |
Valiquette, F. |
| spellingShingle |
Valiquette, F. Solving Local Equivalence Problems with the Equivariant Moving Frame Method Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Valiquette, F. |
| author_sort |
Valiquette, F. |
| title |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_short |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_full |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_fullStr |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_full_unstemmed |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_sort |
solving local equivalence problems with the equivariant moving frame method |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149233 |
| citation_txt |
Solving Local Equivalence Problems with the Equivariant Moving Frame Method / F. Valiquette // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 42 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT valiquettef solvinglocalequivalenceproblemswiththeequivariantmovingframemethod |
| first_indexed |
2023-05-20T17:32:18Z |
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2023-05-20T17:32:18Z |
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1796153516401623040 |