Coframe

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 $v\_k:bigoplus^kT^*Mtobigwedge^kT^*M$, given by $v\_k:(rho\_1,ldots,rho\_k)mapsto\; rho\_1wedgeldotswedgerho\_k$. If $M$ is $n$ dimensional a coframe is given by a section $sigma$ of $bigoplus^nT^*M$ such that $v\_ncircsigmaneq\; 0$. The inverse image under $v\_n$ of the complement of the zero section of $bigwedge^nT^*M$ forms a $GL(n)$ principle bundle over $M$, which is called the coframe bundle.

See also

• Frame fields in general relativity
• Moving frame