The distribution on any Carnot group is left invariant, so pick any set of differential forms at the origin that annihilates the distribution at that point, then left translate it to give a global set of one forms whose kernel is the distribution.

On the Heisenberg group this procedures gives a scalar multiple of the standard contact form.

The distribution on any Carnot group is left invariant, so pick any set of covectors at the origin that annihilates the distribution at that point, then left translate it to give a global set of one forms whose kernel is the distribution.

On the Heisenberg group this procedures gives a scalar multiple of the standard contact form.

The distribution on any Carnot group is left invariant, so pick any set of differential forms at the origin that annihilates the distribution at that point, then left translate it to give a global set of one forms whose kernel is the distribution.

The distribution on any Carnot group is left invariant, so pick any set of differential forms at the origin that annihilates the distribution at that point, then left translate it to give a global set of one forms whose kernel is the distribution.

On the Heisenberg group this procedures gives a scalar multiple of the standard contact form.