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Title: Liftings of vector fields to $1$-forms on the $r$-jet prolongation of the cotangent bundle (English)
Author: Mikulski, W. M.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 3
Year: 2002
Pages: 565-573
Category: math
Summary: For natural numbers $r$ and $n\geq 2$ all natural operators $T_{\vert \Cal M f_n}\rightsquigarrow T^* (J^rT^{*})$ transforming vector fields from $n$-manifolds $M$ into $1$-forms on $J^r T^{*}M=\{j^r_x (\omega)\mid \omega \in \Omega^1(M), x\in M\}$ are classified. A similar problem with fibered manifolds instead of manifolds is discussed. (English)
Keyword: natural bundle
Keyword: natural operator
MSC: 58A20
MSC: 58A32
idZBL: Zbl 1090.58005
idMR: MR1920532
Date available: 2009-01-08T19:25:16Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Doupovec M., Kurek J.: Liftings of tensor fields to the cotangent bundles.Proc. Conf. Differential Geom. and Appl., Brno, 1995, pp.141-150. MR 1406334
Reference: [2] Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry.Springer Verlag, Berlin, 1993. MR 1202431
Reference: [3] Kurek J., Mikulski W.M.: The natural operators lifting $1$-forms to some vector bundle functors.Colloq. Math. (2002), to appear. Zbl 1020.58003, MR 1930803
Reference: [4] Mikulski W.M.: The natural operators $T_{\vert \Cal M f_n} \rightsquigarrow T^* T^{r*}$ and $T_{\vert \Cal M f_n}\rightsquigarrow \Lambda^2 T^*T^{r*}$.Colloq. Math. (2002), to appear. MR 1930256
Reference: [5] Mikulski W.M.: Liftings of $1$-forms to the bundle of affinors.Ann. UMCS Lublin (LV)(A) (2001), 109-113. Zbl 1020.58005, MR 1845255


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