Higher order jet prolongations type gauge natural bundles over vector bundles

Abstract

Let $r\geq 3$ and $m\geq 2$ be natural numbers and $E$ be a vector bundle with $m$-dimensional basis. We find all gauge natural bundles ``similar" to the $r$-jet prolongation bundle $J^rE$ of $E$. We also find all gauge natural bundles ``similar" to the vector $r$-tangent bundle $(J^r_{fl}(E,\R)_0)^*$ of $E$.