Riemannian structures on higher order frame bundles over Riemannian manifolds

(Lobachevskii Journal of Mathematics, Volume XXVII)

We describe all M f_m-natural operators A: Riem → Riem P^r transforming Riemannian structures g on m-dimensional manifolds M into Riemannian structures A(g) on the r-th order frame bundle P^rM=invJ^r₀(R^m, M) over M.