What is "coframe"

n. (context mathematics English) A particular system of covectors

In mathematics, a coframe or coframe field on a smooth manifold M is a system of one-forms or covectors which form a basis of the cotangent bundle at every point. In the exterior algebra of M, one has a natural map from v : ⨁TM → ⋀TM, given by v : (ρ, …, ρ) ↦ ρ ∧ … ∧ ρ. If M is n dimensional a coframe is given by a section σ of ⨁TM such that v ∘ σ ≠ 0. The inverse image under v of the complement of the zero section of ⋀TM forms a GL(n) principal bundle over M, which is called the coframe bundle.