Defining a distribution on a manifold

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I'm stuck on a problem, because I don't know what it means:

Define a distribution $D$ by:

$\omega_1 =0, ... \omega_n =0$

Where the $\omega_i$ is the dual co-frames forms, from the Equations of Structure.

This definition is equivalent to some definition by the Ker of some aplication? Exist a standard argument to prove that $D$ is integrable and parallel?

Thanks!