Jacobi structures on affine bundles

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dc.creatorGrabowski, J.
dc.creatorIglesias, D.
dc.creatorMarrero, J. C.
dc.creatorPadrón, E.
dc.creatorUrbański, P.
dc.date2002-12-04
dc.date2006-03-13
dc.date.accessioned2026-07-07T06:35:32Z
dc.date.available2026-07-07T06:35:32Z
dc.descriptionWe study affine Jacobi structures on an affine bundle $π:A\to M$, i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on $A$ and Lie algebroid structures on the vector bundle $A^+=\bigcup_{p\in M}Aff(A_p,\R)$ of affine functionals. Some examples and applications, also for the linear case, are discussed. For a special type of affine Jacobi structures which are canonically exhibited (strongly-affine or affine-homogeneous Jacobi structures) over a real vector space of finite dimension, we describe the leaves of its characteristic foliation as the orbits of an affine representation. These affine Jacobi structures can be viewed as an analog of the Kostant-Arnold-Liouville linear Poisson structure on the dual space of a real finite-dimensional Lie algebra.
dc.description26 pages; minor changes, one reference added. The final version to appear in Acta Math. Sinica, English Series
dc.identifierhttps://arxiv.org/abs/math/0212052
dc.identifierhttp://arxiv.org/abs/math/0212052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99822
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subject53D17; 53D05; 81S10
dc.titleJacobi structures on affine bundles
dc.typetext

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