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

On the Differential Geometry of Coframe Bundle with Cheeger-Gromoll Metric

“…x M of M at x [5]. We denote by π the natural projection of F * (M ) to M defined by π(x, u * ) = x.…”

“…x M can be expressed uniquely in the form X α = X α i (dx i ) x . From mentioned above it follows that is a system of local coordinates in F * (M ) (see, [5]), that is F * (M ) is a C ∞ − manifold of dimension n + n 2 . We note that indices i, j, k, ..., α, β, γ, ... have range in {1, 2, ..., n}, while indices A, B, C, ... have range in 1, ..., n, n + 1, ..., n + n 2 .…”