On a generalization of the boundle of linear frames (Q2568734)

The author constructs a generalization of the bundle of linear frames on a manifold \(M\). Such a bundle turns out to be a principal bundle on the product \(M\times G_{n,p}\), where \(G_{n,p}\) is the Grassmann manifold of \(p\)-dimensional subspaces in \(\mathbb R^n\). Some considerations on connections on the above bundle are also provided. The above construction seems to be closely related to the construction of the manifold of contact elements [see \textit{I. Kolář, P. Michor} and \textit{J. Slovák}, Natural operations in differential geometry, Springer-Verlag (1993; Zbl 0782.53013)].