Some notes on the differential geometry of linear coframe bundle of a Riemannian manifold

In this paper, we construct f-structures F-alpha, 1 <= alpha <= n , (F) over tilde and (F) over bar on the linear coframe bundle F* (M) of the Riemannian manifold M. It is proved that these structures are adapted with the diagonal lift (D) g of the Riemannian metric g of the manifold M into the linear coframe bundle F*(M). Also we study the integrability and parallelism of the f-structures F-alpha, 1 <= alpha <= n, (F) over tilde and (F) over bar.