We classify all natural operators lifting linear vector fields on vector bundles to vector fields on vertical fiber product preserving gauge bundles over vector bundles. We explain this result for some known examples of such bundles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-5, author = {J. Kurek and W. M. Mikulski}, title = {Lifting of linear vector fields to fiber product preserving vertical gauge bundles}, journal = {Colloquium Mathematicae}, volume = {103}, year = {2005}, pages = {33-40}, zbl = {1086.58002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-5} }
J. Kurek; W. M. Mikulski. Lifting of linear vector fields to fiber product preserving vertical gauge bundles. Colloquium Mathematicae, Tome 103 (2005) pp. 33-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-1-5/