# Coframe

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In mathematics, a **coframe** or **coframe field** on a smooth manifold is a system of one-forms or covectors which form a basis of the cotangent bundle at every point. In the exterior algebra of , one has a natural map from , given by . If is dimensional a coframe is given by a section of such that . The inverse image under of the complement of the zero section of forms a principal bundle over , which is called the coframe bundle.