Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle

Mikulski, Włodzimierz M.. "Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 565-573. <http://eudml.org/doc/248956>.

@article{Mikulski2002,
abstract = {For natural numbers $r$ and $n\ge 2$ all natural operators $T_\{\vert \mathcal \{M\} f_n\}\rightsquigarrow T^* (J^rT^\{*\})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^\{*\}M=\lbrace j^r_x (\omega )\mid \omega \in \Omega ^1(M), x\in M\rbrace $ are classified. A similar problem with fibered manifolds instead of manifolds is discussed.},
author = {Mikulski, Włodzimierz M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {natural bundle; natural operator; natural bundle; natural operator; cotangent bundle},
language = {eng},
number = {3},
pages = {565-573},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle},
url = {http://eudml.org/doc/248956},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 565
EP - 573
AB - For natural numbers $r$ and $n\ge 2$ all natural operators $T_{\vert \mathcal {M} f_n}\rightsquigarrow T^* (J^rT^{*})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^{*}M=\lbrace j^r_x (\omega )\mid \omega \in \Omega ^1(M), x\in M\rbrace $ are classified. A similar problem with fibered manifolds instead of manifolds is discussed.
LA - eng
KW - natural bundle; natural operator; natural bundle; natural operator; cotangent bundle
UR - http://eudml.org/doc/248956
ER -

References

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Doupovec M., Kurek J., Liftings of tensor fields to the cotangent bundles, Proc. Conf. Differential Geom. and Appl., Brno, 1995, pp.141-150. MR1406334
Kolář I., Michor P.W., Slovák J., Natural Operations in Differential Geometry, Springer Verlag, Berlin, 1993. MR1202431
Kurek J., Mikulski W.M., The natural operators lifting $1$ -forms to some vector bundle functors, Colloq. Math. (2002), to appear. Zbl1020.58003 MR1930803
Mikulski W.M., The natural operators $T_{| ℳ f_{n}} ⇝ T^{*} T^{r *}$ and $T_{| ℳ f_{n}} ⇝ Λ^{2} T^{*} T^{r *}$ , Colloq. Math. (2002), to appear. MR1930256
Mikulski W.M., Liftings of $1$ -forms to the bundle of affinors, Ann. UMCS Lublin (LV)(A) (2001), 109-113. (2001) Zbl1020.58005 MR1845255

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