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On Liouville forms. (English) Zbl 0981.53071

Grabowski, Janusz (ed.) et al., Poisson geometry. Stanisław Zakrzewski in memoriam. Warszawa: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 51, 151-164 (2000).
Summary: We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration \(\pi:E\to M\). These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.
For the entire collection see [Zbl 0936.00035].

MSC:

53D05 Symplectic manifolds (general theory)
70H05 Hamilton’s equations
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D20 Momentum maps; symplectic reduction
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