A coframe refers to a mathematical construct in differential geometry and is often used in the context of differentiable manifolds. Specifically, a coframe is a set of differential one-forms that provide a dual basis to a frame, which is a set of tangent vectors. Here's a more detailed breakdown: 1. **Frame**: Given a manifold, a frame at a point is essentially a set of linearly independent tangent vectors that span the tangent space at that point.
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A coframe dual to a local frame of the tangent bundle is the corresponding local frame of the cotangent bundle. Its elements are differential one-forms. Applying the coframe to covariant derivatives of the frame extracts the connection one-forms; applying it to the torsion tensor extracts the torsion forms.