We prove that the so-called complete lifting of tangent valued forms from a manifold $M$ to an arbitrary Weil bundle over $M$ preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.
@article{107533,
author = {Antonella Cabras and Ivan Kol\'a\v r},
title = {Prolongation of tangent valued forms to Weil bundles},
journal = {Archivum Mathematicum},
volume = {031},
year = {1995},
pages = {139-145},
zbl = {0843.53021},
mrnumber = {1357981},
language = {en},
url = {http://dml.mathdoc.fr/item/107533}
}
Cabras, Antonella; Kolář, Ivan. Prolongation of tangent valued forms to Weil bundles. Archivum Mathematicum, Tome 031 (1995) pp. 139-145. http://gdmltest.u-ga.fr/item/107533/
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