The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended -th order tangent bundle over a manifold ) are linear combinations (the coefficients of which are smooth functions on ) of four natural affinors defined in this work.
@article{701509,
title = {Natural affinors on the extended $r$-th order tangent bundles},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {1993},
pages = {[95]-100},
mrnumber = {MR1246623},
zbl = {0791.58009},
url = {http://dml.mathdoc.fr/item/701509}
}
Gancarzewicz, Jacek; Kolář, Ivan. Natural affinors on the extended $r$-th order tangent bundles, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1993), pp. [95]-100. http://gdmltest.u-ga.fr/item/701509/