Lifting connections to the r-jet prolongation of the cotangent bundle

Włodzimierz M. Mikulski
2015 Mathematics for applications  
We show that the problem of finding all Mfm-natural operators C : Q QJ r T * lifting classical linear connections ∇ on m-manifolds M into classical linear connections C M (∇) on the r-jet prolongation J r T * M of the cotangent bundle T * M of M can be reduced to that of finding all Mfm-natural operators D : Q p T ⊗ q T * sending classical linear connections ∇ on M into tensor fields D M (∇) of type (p, q) on M . MSC (2010): primary 58A20; secondary 58A32.
doi:10.13164/ma.2014.09 fatcat:h336ofwijrhulfm2d6kw43unca