Geodesic
The natural operators lifting connections to higher order cotangent bundles
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 509-518.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We prove that the problem of finding all ${\mathcal {M} f_m}$-natural operators ${C\colon Q\rightsquigarrow QT^{r*}}$ lifting classical linear connections $\nabla $ on $m$-manifolds $M$ into classical linear connections $C_M(\nabla )$ on the $r$-th order cotangent bundle $T^{r*}M=J^r(M,\mathbb R )_0$ of $M$ can be reduced to the well known one of describing all $\mathcal {M} f_m$-natural operators $D\colon Q\rightsquigarrow \bigotimes ^pT\otimes \bigotimes ^qT^*$ sending classical linear connections $\nabla $ on $m$-manifolds $M$ into tensor fields $D_M(\nabla )$ of type $(p,q)$ on $M$.
DOI : 10.1007/s10587-014-0116-7
Classification : 53C05, 58A20, 58A32
Keywords: classical linear connection; natural operator 
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Mikulski, Włodzimierz M. The natural operators lifting connections to higher order cotangent bundles. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 509-518. doi : 10.1007/s10587-014-0116-7. http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0116-7/

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