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 $v_{k} : ⨁^{k} T^{*} M \to \overset{k}{⋀} T^{*} M$ , given by $v_{k} : (ρ_{1}, \dots, ρ_{k}) \mapsto ρ_{1} \land \dots \land ρ_{k}$ . If $M$ is $n$ dimensional, a coframe is given by a section $σ$ of $⨁^{n} T^{*} M$ such that $v_{n} \circ σ \neq 0$ . The inverse image under $v_{n}$ of the complement of the zero section of $\overset{n}{⋀} T^{*} M$ forms a $G L (n)$ principal bundle over $M$ , which is called the coframe bundle.

References

↑ "Structure coefficients of a coframe". Mathematics Stack Exchange. Retrieved 2024-01-19.

Sources

Manuel Tecchiolli (2019). "On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review". Universe. 5(10) (Torsion Gravity): 206. arXiv:2008.08314. Bibcode:2019Univ....5..206T. doi:10.3390/universe5100206.

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[1] "Structure coefficients of a coframe". Mathematics Stack Exchange. Retrieved 2024-01-19.

Coframe

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References

Sources