Singularity Classes of Special 2-Flags
In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations deal with rank-2 distributions and are responsible for the appearance of...
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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149107 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Singularity Classes of Special 2-Flags / P. Mormul // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
Репозитарії
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irk-123456789-1491072019-02-20T01:25:22Z Singularity Classes of Special 2-Flags Mormul, P. In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations deal with rank-2 distributions and are responsible for the appearance of the Goursat distributions. Similarly, the so-called special multi-flags are generated in the result of successive applications of gCp's. Singularities of such distributions turn out to be very rich, although without functional moduli of the local classification. The paper focuses on special 2-flags, obtained by sequences of gCp's applied to rank-3 distributions. A stratification of germs of special 2-flags of all lengths into singularity classes is constructed. This stratification provides invariant geometric significance to the vast family of local polynomial pseudo-normal forms for special 2-flags introduced earlier in [Mormul P., Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]. This is the main contribution of the present paper. The singularity classes endow those multi-parameter normal forms, which were obtained just as a by-product of sequences of gCp's, with a geometrical meaning. 2009 Article Singularity Classes of Special 2-Flags / P. Mormul // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 58A15; 58A17; 58A30 http://dspace.nbuv.gov.ua/handle/123456789/149107 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 |
In the paper we discuss certain classes of vector distributions in the tangent bundles to manifolds, obtained by series of applications of the so-called generalized Cartan prolongations (gCp). The classical Cartan prolongations deal with rank-2 distributions and are responsible for the appearance of the Goursat distributions. Similarly, the so-called special multi-flags are generated in the result of successive applications of gCp's. Singularities of such distributions turn out to be very rich, although without functional moduli of the local classification. The paper focuses on special 2-flags, obtained by sequences of gCp's applied to rank-3 distributions. A stratification of germs of special 2-flags of all lengths into singularity classes is constructed. This stratification provides invariant geometric significance to the vast family of local polynomial pseudo-normal forms for special 2-flags introduced earlier in [Mormul P., Banach Center Publ., Vol. 65, Polish Acad. Sci., Warsaw, 2004, 157-178]. This is the main contribution of the present paper. The singularity classes endow those multi-parameter normal forms, which were obtained just as a by-product of sequences of gCp's, with a geometrical meaning. |
| format |
Article |
| author |
Mormul, P. |
| spellingShingle |
Mormul, P. Singularity Classes of Special 2-Flags Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Mormul, P. |
| author_sort |
Mormul, P. |
| title |
Singularity Classes of Special 2-Flags |
| title_short |
Singularity Classes of Special 2-Flags |
| title_full |
Singularity Classes of Special 2-Flags |
| title_fullStr |
Singularity Classes of Special 2-Flags |
| title_full_unstemmed |
Singularity Classes of Special 2-Flags |
| title_sort |
singularity classes of special 2-flags |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149107 |
| citation_txt |
Singularity Classes of Special 2-Flags / P. Mormul // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT mormulp singularityclassesofspecial2flags |
| first_indexed |
2023-05-20T17:32:09Z |
| last_indexed |
2023-05-20T17:32:09Z |
| _version_ |
1796153520849682432 |