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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of a one-form

**Physics Forums | Science Articles, Homework Help, Discussion**