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Keywords:
higher order linear connection; natural operator
higher order linear connection; natural operator
Summary:
We describe how find all $\mathcal Mf_m$-natural operators $D$ transforming torsion free classical linear connections $\nabla $ on $m$-manifolds $M$ into $r$-th order linear connections $D(\nabla )$ on $M$.
References:
[1] Kolář I.: Torsion-free connections on higher order frame bundles. in New Development in Differential Geometry, Proceedings (Conference in Debrecen), Kluwer 1996, 233–241. MR 1377287
[2] Kolář I.: On the torsion-free connections on higher order frame bundles. Publ. Math. Debrecen 67 (3-4), (2005), 373–379. MR 2162129 | Zbl 1083.53026
[3] Kolář I., Michor P. W., Slovák J.: Natural Operations In Differential Geometry. Springer-Verlag Berlin 1993. MR 1202431 | Zbl 0782.53013
[4] Paluszny M., Zajtz A.: Foundations of differential geometry of natural bundles. Lecture Notes Univ. Caracas, 1984.
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