2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75673Let $FM,\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\mathrm{Diff}M$-invariant connection form on $J^1\mathcal{M}_M\times_MFM\to J^1\mathcal{M}_M$, which is Riemannian with respect to the universal metric on $J^1\mathcal{M}_M\times_MTM$, is proved. Aplications to the construction of universal Pontryagin and Euler forms, are given.Differential GeometryPrimary 53A55; Secondary 53B05, 53B21, 57R20, 58A20, 58D19text