منابع مشابه
Integrability of Jacobi Structures
We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu [20]. The methods used are those of CrainicFernandes on A-paths and monodr...
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Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a particular case, the recently introduced generalized Poisson structures. The linear case on simple group man-ifolds is also studied and non-trivial examples (differe...
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Using E1(M)-Dirac structures, a notion introduced by A. Wade, we obtain conditions under which a submanifold of a Jacobi manifold has an induced Jacobi structure, generalizing the result obtained by Courant for Dirac structures and submanifolds of a Poisson manifold.
متن کاملIntegration of Dirac-Jacobi structures
We study precontact groupoids whose infinitesimal counterparts are Dirac-Jacobi structures. These geometric objects generalize contact groupoids. We also explain the relationship between precontact groupoids and homogeneous presymplectic groupoids. Finally, we present some examples of precontact groupoids.
متن کاملJacobi structures on affine bundles
We study affine Jacobi structures (brackets) on an affine bundle π : A→M , i.e. Jacobi brackets that close on affine functions. We prove that if the rank of A is non-zero, there is a one-to-one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A = ⋃ p∈M Aff(Ap,R) of affine functionals. In the case rank A = 0, it is shown that there is a one-t...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2005
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2040347