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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149107 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Singularity Classes of Special 2-Flags / P. Mormul // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862723036034105344 |
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| author | Mormul, P. |
| author_facet | Mormul, P. |
| citation_txt | Singularity Classes of Special 2-Flags / P. Mormul // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T18:39:02Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149107 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:39:02Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Mormul, P. 2019-02-19T17:26:02Z 2019-02-19T17:26:02Z 2009 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 https://nasplib.isofts.kiev.ua/handle/123456789/149107 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. This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”. The author was supported by Polish Grant MNSzW N N 201 397 937. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Singularity Classes of Special 2-Flags Article published earlier |
| spellingShingle | Singularity Classes of Special 2-Flags Mormul, P. |
| title | 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_short | Singularity Classes of Special 2-Flags |
| title_sort | singularity classes of special 2-flags |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149107 |
| work_keys_str_mv | AT mormulp singularityclassesofspecial2flags |