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- W2114429346 abstract "An analogue of the Hofer metric $varrho_H$ on the Hamiltonian group $Ham(M,Lambda)$ of a Poisson manifold $(M,Lambda)$ can be defined but there is the problem of its non-degeneracy. First we observe that $varrho_H$ is a genuine metric on $Ham(M,Lambda)$ when the union of all closed leaves (as subsets of $M$) of the corresponding symplectic foliation is dense. Next we deal with the important class of integrable Poisson manifolds. Recall that a Poisson manifold is called integrable if it can be realized as the space of units of a symplectic groupoid. Our main result states that $varrho_H$ is a Hofer type metric for every Poisson manifold which admits a Hausdorff integration." @default.
- W2114429346 created "2016-06-24" @default.
- W2114429346 creator A5035073954 @default.
- W2114429346 date "2015-07-16" @default.
- W2114429346 modified "2023-10-01" @default.
- W2114429346 title "On the existence of a Hofer type metric for Poisson manifolds" @default.
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