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Remarks on contact and Jacobi geometry

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dc.abstract.enWe 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)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.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorGrabowski, Janusz
dc.contributor.authorGrabowska, Katarzyna
dc.contributor.authorBruce, Andrew
dc.date.accessioned2024-01-25T19:11:14Z
dc.date.available2024-01-25T19:11:14Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.identifier.doi10.3842/SIGMA.2017.059
dc.identifier.issn1815-0659
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/118361
dc.languageeng
dc.pbn.affiliationphysical sciences
dc.relation.ispartofSymmetry, Integrability and Geometry - Methods and Applications
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.ensymplectic structures
dc.subject.encontact structures
dc.subject.enPoisson structures
dc.subject.enJacobi structures
dc.subject.enprincipal bundles
dc.subject.enLie groupoids
dc.subject.ensymplectic groupoids.
dc.titleRemarks on contact and Jacobi geometry
dc.typeJournalArticle
dspace.entity.typePublication