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

Jan Kurek; Wlodzimierz M. Mikulski

Extracta Mathematicae (2006)

- Volume: 21, Issue: 2, page 159-166
- ISSN: 0213-8743

## Access Full Article

top## Abstract

top## How to cite

topKurek, 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 -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.