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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149233 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716117894561792 |
|---|---|
| author | Valiquette, F. |
| author_facet | Valiquette, F. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:03:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149233 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:03:09Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Valiquette, F. 2019-02-19T19:04:08Z 2019-02-19T19:04:08Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/149233 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. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants
 and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Solving Local Equivalence Problems with the Equivariant Moving Frame Method Article published earlier |
| spellingShingle | Solving Local Equivalence Problems with the Equivariant Moving Frame Method Valiquette, F. |
| title | 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_short | Solving Local Equivalence Problems with the Equivariant Moving Frame Method |
| title_sort | solving local equivalence problems with the equivariant moving frame method |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149233 |
| work_keys_str_mv | AT valiquettef solvinglocalequivalenceproblemswiththeequivariantmovingframemethod |