The horizontal distribution in the **Heisenberg group** is the kernel of the standard contact form:
$$
\alpha = dt + 2 \sum_{j=1}^n (x_j \, dy_j - y_j \, dx_j).
$$

Question.Can one describe horizontal distribution in anyCarnot groupin terms of kernels of some $1$-forms?

I believe the answer should be in the positive and I am looking for references for explicit constructions of such forms so that in the case of the Heisenberg group these constructions would give the contact form.