Remarks on Contact and Jacobi Geometry
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148728 |
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| Cite this: | Remarks on Contact and Jacobi Geometry / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 47 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-148728 |
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Bruce, A.J. Grabowska, K. Grabowski, J. 2019-02-18T18:12:47Z 2019-02-18T18:12:47Z 2017 Remarks on Contact and Jacobi Geometry / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 47 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D05; 53D10; 53D17; 58E40; 58H05 DOI:10.3842/SIGMA.2017.059 https://nasplib.isofts.kiev.ua/handle/123456789/148728 We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,R)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory. The authors are indebted to the anonymous referees whose comments have served to improve the content and presentation of this paper. The research of K. Grabowska and J. Grabowski was funded by the Polish National Science Centre grant under the contract number DEC2012/06/A/ST1/00256. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Remarks on Contact and Jacobi Geometry Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Remarks on Contact and Jacobi Geometry |
| spellingShingle |
Remarks on Contact and Jacobi Geometry Bruce, A.J. Grabowska, K. Grabowski, J. |
| title_short |
Remarks on Contact and Jacobi Geometry |
| title_full |
Remarks on Contact and Jacobi Geometry |
| title_fullStr |
Remarks on Contact and Jacobi Geometry |
| title_full_unstemmed |
Remarks on Contact and Jacobi Geometry |
| title_sort |
remarks on contact and jacobi geometry |
| author |
Bruce, A.J. Grabowska, K. Grabowski, J. |
| author_facet |
Bruce, A.J. Grabowska, K. Grabowski, J. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,R)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148728 |
| citation_txt |
Remarks on Contact and Jacobi Geometry / A.J. Bruce, K. Grabowska, J. Grabowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 47 назв. — англ. |
| work_keys_str_mv |
AT bruceaj remarksoncontactandjacobigeometry AT grabowskak remarksoncontactandjacobigeometry AT grabowskij remarksoncontactandjacobigeometry |
| first_indexed |
2025-12-07T21:13:24Z |
| last_indexed |
2025-12-07T21:13:24Z |
| _version_ |
1850885542962528256 |