Natural maps on the iterated jet prolongation of a fibred manifold (original) (raw)

This work explores natural transformations of the second iterated jet prolongation of a fibred manifold with respect to a linear connection on the base manifold. The authors first identify all natural transformations of the functor corresponding to the jet prolongation, resulting in the discovery of two 3-parameter families of transformations. The findings highlight the significance of a particular involution and its implications for constructing connections on jet prolongations, which are important in geometric and physical theories.