|
SIGMA, 2017, том 13, 059, 22 страниц
(Mi sigma1259)
|
|
|
|
Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Remarks on Contact and Jacobi Geometry
Andrew James Brucea, Katarzyna Grabowskab, Janusz Grabowskic a Mathematics Research Unit, University of Luxembourg, Luxembourg
b Faculty of Physics, University of Warsaw, Poland
c Institute of Mathematics, Polish Academy of Sciences, Poland
Аннотация:
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 $GL(1,{\mathbb R})$-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.
Ключевые слова:
symplectic structures; contact structures; Poisson structures; Jacobi structures; principal bundles; Lie groupoids; symplectic groupoids.
Финансовая поддержка |
Номер гранта |
National Science Centre (Narodowe Centrum Nauki)  |
DEC-2012/06/A/ST1/00256 |
The research of K. Grabowska and J. Grabowski was funded by the Polish National Science Centre grant under the contract number DEC-2012/06/A/ST1/00256. |
DOI:
https://doi.org/10.3842/SIGMA.2017.059
Полный текст:
PDF файл (476 kB)
Полный текст:
http://www.emis.de/.../059
Список литературы:
PDF файл
HTML файл
Реферативные базы данных:
Тип публикации:
Статья
MSC: 53D05; 53D10; 53D17; 58E40; 58H05 Поступила: 16 января 2017 г.; в окончательном варианте 17 июля 2017 г.; опубликована 26 июля 2017 г.
Язык публикации: английский
Образец цитирования:
Andrew James Bruce, Katarzyna Grabowska, Janusz Grabowski, “Remarks on Contact and Jacobi Geometry”, SIGMA, 13 (2017), 059, 22 pp.
Цитирование в формате AMSBIB
\RBibitem{BruGraGra17}
\by Andrew~James~Bruce, Katarzyna~Grabowska, Janusz~Grabowski
\paper Remarks on Contact and Jacobi Geometry
\jour SIGMA
\yr 2017
\vol 13
\papernumber 059
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma1259}
\crossref{https://doi.org/10.3842/SIGMA.2017.059}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000406498400001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026847762}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/sigma1259 http://mi.mathnet.ru/rus/sigma/v13/p59
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
-
A. Sergyeyev, “New integrable (3+1)-dimensional systems and contact geometry”, Lett. Math. Phys., 108:2 (2018), 359–376
-
A. K. Prikarpatskii, “On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems”, SIGMA, 14 (2018), 023, 15 pp.
-
K. Grabowska, J. Grabowski, “$n$-Tuple principal bundles”, Int. J. Geom. Methods Mod. Phys., 15:12 (2018), 1850211
-
Bravetti A., “Contact Geometry and Thermodynamics”, Int. J. Geom. Methods Mod. Phys., 16:1, SI (2019), 1940003
-
Das A., “Gauge Transformations of Jacobi Structures and Contact Groupoids”, Math. Phys. Anal. Geom., 22:2 (2019), 11
|
Просмотров: |
Эта страница: | 153 | Полный текст: | 7 | Литература: | 10 |
|