Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators
Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-fre...
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| Дата: | 2017 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148630 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. |
Репозитарії
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irk-123456789-1486302019-02-19T01:30:06Z Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators Salazar, M.A. Sepe, D. Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones. 2017 Article Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D10; 53D17; 53D20; 37J15 DOI:10.3842/SIGMA.2017.033 http://dspace.nbuv.gov.ua/handle/123456789/148630 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 |
Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones. |
| format |
Article |
| author |
Salazar, M.A. Sepe, D. |
| spellingShingle |
Salazar, M.A. Sepe, D. Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Salazar, M.A. Sepe, D. |
| author_sort |
Salazar, M.A. |
| title |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_short |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_full |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_fullStr |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_full_unstemmed |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators |
| title_sort |
contact isotropic realisations of jacobi manifolds via spencer operators |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148630 |
| citation_txt |
Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators / M.A. Salazar, D. Sepe // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 33 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT salazarma contactisotropicrealisationsofjacobimanifoldsviaspenceroperators AT seped contactisotropicrealisationsofjacobimanifoldsviaspenceroperators |
| first_indexed |
2023-05-20T17:30:32Z |
| last_indexed |
2023-05-20T17:30:32Z |
| _version_ |
1796153460268204032 |