Natural transformations of vector fields on manifolds to vector fields on tangent bundles (Q1110818)

The main result of the paper is that all first order natural operators transforming every vector field on a manifold M into a vector field on its tangent bundle form a 3-parameter family linearly generated by the flow operator, the vertical lift and the Liouville vector field. [The reviewer has recently deduced that the same result holds under no assumption on the order of the operators, Ann. Global Anal. Geom. 6, 109- 117 (1988)]. The author also determines all second order natural transformations of a linear symmetric connection on M and a vector field on M into a vector field on TM.