A one-form is something of the form(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\omega=\omega_\mu dx^\mu[/tex]

But is it necessary that the components [tex]\omega_\mu[/tex] be components of a type (0,1) tensor?

For instance, the connection one-form is defined to be

[tex]{\omega^{\alpha}}_\beta = {\Gamma^\alpha}_{\gamma\beta} \hat{\theta}^\gamma[/tex]

where [tex]\hat{\theta}^\gamma[/tex] is a basis of the dual tangent space, though not necessarily a coordinate basis. Here the components [tex]{\Gamma^\alpha}_{\gamma\beta} [/tex]--the connection coefficients, i.e., Christoffel symbols-- not only are not those of a type (0,1) tensor, they are not even those of a tensor.

So is this legitimately a one-form?

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# Definition of a one-form

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