We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr 0 (R;M) of a symplectic manifold (M, ω). As a corollary we deduce that all canonical symplectic structures Λ(ω) on TrM over a symplectic manifold (M, ω) are of the form Λ(ω) = Σr k=0 αkω(k) for all real numbers αk with αr ≠ 0, where ω(k) is the (k)-lift (in the sense of A. Morimoto) of ω to TrM.
@article{urn:eudml:doc:41856,
title = {Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.},
journal = {Extracta Mathematicae},
volume = {21},
year = {2006},
pages = {159-166},
zbl = {1141.58002},
mrnumber = {MR2292745},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41856}
}
Kurek, Jan; Mikulski, Wlodzimierz M. Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.. Extracta Mathematicae, Tome 21 (2006) pp. 159-166. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41856/