 One can start with the anti-holomorphic vector field formula_54 on the Heisenberg group given by

The vector field defined above has two linearly independent first integrals.That is there are two solutions to the homogeneous equation,

Since we are in real dimension three the formal integrability condition is simply,

which is automatic.Notice the Levi form is strictly positive definite as a simple calculation gives,

where the holomorphic vector field L is given by,

The first integrals which are linearly independent allow us to realize the CR structure as a graph in formula_4 given by

The CR structure then is seen to be nothing but the restriction of the Complex structure of formula_4 to the graph.