Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold
A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The s...
- Autores:
-
Arias, F.A
Malakhaltsev, M.
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/12265
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/12265
- Palabra clave:
- $G$-structure with singularities
Contact structure
Sub-Riemannian structure
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| title |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| spellingShingle |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold $G$-structure with singularities Contact structure Sub-Riemannian structure |
| title_short |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| title_full |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| title_fullStr |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| title_full_unstemmed |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| title_sort |
Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold |
| dc.creator.fl_str_mv |
Arias, F.A Malakhaltsev, M. |
| dc.contributor.author.none.fl_str_mv |
Arias, F.A Malakhaltsev, M. |
| dc.subject.keywords.spa.fl_str_mv |
$G$-structure with singularities Contact structure Sub-Riemannian structure |
| topic |
$G$-structure with singularities Contact structure Sub-Riemannian structure |
| description |
A contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii. We consider a contact structure with singularities as a G-structure with singularities, we find some topological and differential invariants of singularities of contact structure and establish their relation to the invariants found by B. Jakubczyk and M. Zhitomirskii. © 2020, Pleiades Publishing, Ltd. |
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2020 |
| dc.date.issued.none.fl_str_mv |
2020-12 |
| dc.date.accessioned.none.fl_str_mv |
2023-07-21T15:35:23Z |
| dc.date.available.none.fl_str_mv |
2023-07-21T15:35:23Z |
| dc.date.submitted.none.fl_str_mv |
2023-07 |
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Arias, F.A., Malakhaltsev, M. Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold. Lobachevskii J Math 41, 2415–2426 (2020). https://doi.org/10.1134/S1995080220120070 |
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https://hdl.handle.net/20.500.12585/12265 |
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10.1134/S1995080220120070 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Arias, F.A., Malakhaltsev, M. Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold. Lobachevskii J Math 41, 2415–2426 (2020). https://doi.org/10.1134/S1995080220120070 10.1134/S1995080220120070 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/12265 |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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openAccess |
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12 páginas |
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Cartagena de Indias |
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Campus Tecnológico |
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Lobachevskii Journal of Mathematics - Vol. 41 No.2 (2020) |
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Universidad Tecnológica de Bolívar |
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Arias, F.Ac440aee6-84a2-44dd-a512-506308c000a4Malakhaltsev, M.2750b343-25d1-4546-92ea-5122b8f40ea82023-07-21T15:35:23Z2023-07-21T15:35:23Z2020-122023-07Arias, F.A., Malakhaltsev, M. Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifold. Lobachevskii J Math 41, 2415–2426 (2020). https://doi.org/10.1134/S1995080220120070https://hdl.handle.net/20.500.12585/1226510.1134/S1995080220120070Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarA contact structure on a three-dimensional manifold is a two-dimensional distribution on this manifold which satisfies the condition of complete non-integrability. If the distribution fails to satisfy this condition at points of some submanifold, we have a contact structure with singularities. The singularities of contact structures were studied by J. Martinet, B. Jakubczyk and M. Zhitomirskii. We consider a contact structure with singularities as a G-structure with singularities, we find some topological and differential invariants of singularities of contact structure and establish their relation to the invariants found by B. Jakubczyk and M. Zhitomirskii. © 2020, Pleiades Publishing, Ltd.12 páginasPdfapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Lobachevskii Journal of Mathematics - Vol. 41 No.2 (2020)Topological and Differential Invariants of Singularities of Contact Structure on a Three-Dimensional Manifoldinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/drafthttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_b1a7d7d4d402bccehttp://purl.org/coar/resource_type/c_2df8fbb1$G$-structure with singularitiesContact structureSub-Riemannian structureCartagena de IndiasCampus TecnológicoMartinet, J. Sur les singularités des formes différentielles (1970) Ann. Inst. Fourier (Grenoble), 20, pp. 95-178. Cited 98 times.Jakubczyk, B., Zhitomirskii, M. Local reduction theorems and invariants for singular contact structures (2001) Annales de l'Institut Fourier, 51 (1), pp. 237-295. Cited 8 times. http://annalif.ujf-grenoble.fr/ doi: 10.5802/aif.1823Arteaga B., J.R., Malakhaltsev, M.A. Symmetries of sub-Riemannian surfaces (2011) Journal of Geometry and Physics, 61 (1), pp. 290-308. Cited 5 times. doi: 10.1016/j.geomphys.2010.09.024Arias Amaya, F.A., Malakhaltsev, M. Topological Invariants of Principal G-Bundles with Singularities (Open Access) (2018) Lobachevskii Journal of Mathematics, 39 (5), pp. 623-633. http://www.springer.com/math/journal/12202 doi: 10.1134/S1995080218050013Kobayashi, S., Nomizu, K. (1996) Foundations of Differential Geometry, Wiley Classics Library, 1. Cited 6637 times. (Wiley, New York,), VolMontgomery, R. A Tour of Subriemannian Geometries, Their Geodesics and Applications (2002) Of Mathematical Surveys and Monographs, 91. Cited 514 times. 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