This paper contains a classification of all linear liftings of symmetric tensor fields of type (1,2) on n-dimensional manifolds to any tensor fields of type (1,2) on Weil bundles under the condition that n ≥ 3.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-2, author = {Jacek D\k ebecki}, title = {Linear liftings of symmetric tensor fields of type (1,2) to Weil bundles}, journal = {Annales Polonici Mathematici}, volume = {92}, year = {2007}, pages = {13-27}, zbl = {1131.58004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-2} }
Jacek Dębecki. Linear liftings of symmetric tensor fields of type (1,2) to Weil bundles. Annales Polonici Mathematici, Tome 92 (2007) pp. 13-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap92-1-2/