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Keywords:
natural bundle; natural operator
natural bundle; natural operator
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.
References:
[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
[2] Kolář I., Michor P.W., Slovák J.: Natural Operations in Differential Geometry. Springer Verlag, Berlin, 1993. MR 1202431
[3] Kurek J., Mikulski W.M.: The natural operators lifting $1$-forms to some vector bundle functors. Colloq. Math. (2002), to appear. MR 1930803 | Zbl 1020.58003
[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
[5] Mikulski W.M.: Liftings of $1$-forms to the bundle of affinors. Ann. UMCS Lublin (LV)(A) (2001), 109-113. MR 1845255 | Zbl 1020.58005
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