Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.

Kurek, Jan, and Mikulski, Wlodzimierz M.. "Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.." Extracta Mathematicae 21.2 (2006): 159-166. <http://eudml.org/doc/41856>.

@article{Kurek2006,
abstract = {We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (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) = Σrk=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.},
author = {Kurek, Jan, Mikulski, Wlodzimierz M.},
journal = {Extracta Mathematicae},
keywords = {Variedades diferenciables; Jets; Variedad simpléctica; natural operators; symplectic structures; higher order tangent spaces},
language = {eng},
number = {2},
pages = {159-166},
title = {Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.},
url = {http://eudml.org/doc/41856},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Kurek, Jan
AU - Mikulski, Wlodzimierz M.
TI - Canonical symplectic structures on the r-th order tangent bundle of a symplectic manifold.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 2
SP - 159
EP - 166
AB - We describe all canonical 2-forms Λ(ω) on the r-th order tangent bundle TrM = Jr0 (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) = Σrk=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.
LA - eng
KW - Variedades diferenciables; Jets; Variedad simpléctica; natural operators; symplectic structures; higher order tangent spaces
UR - http://eudml.org/doc/41856
ER -