Szczegóły publikacji
Opis bibliograficzny
On the existence of a Hofer type metric for Poisson manifolds / Tomasz RYBICKI // International Journal of Mathematics ; ISSN 0129-167X. — 2016 — vol. 27 no. 9, s.1650075 -1–1650075-16. — Bibliogr. s. 1650075-15–1650075-16
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 102389 |
|---|---|
| Data dodania do BaDAP | 2016-12-21 |
| DOI | 10.1142/S0129167X16500750 |
| Rok publikacji | 2016 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | International Journal of Mathematics |
Abstract
An analogue of the Hofer metric on the Hamiltonian group of a Poisson manifold can be defined, but there is the problem of its nondegeneracy. First, we observe that is a genuine metric on , when the union of all proper leaves 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 is a Hofer type metric for every Poisson manifold, which admits a Hausdorff integration.