The CR structure then is seen to be nothing but the restriction of the Complex structure of formula_4 to the graph. Nirenberg constructs a single, non-vanishing complex vector field formula_63 defined in a neighborhood of the origin in formula_64 He then shows that if formula_65, then formula_66 has to be a constant. Thus the vector field formula_67 has no first integrals. The vector field formula_67 is created from the anti-holomorphic vector field for the Heisenberg group displayed above by perturbing it by a smooth complex-valued function formula_69 as displayed below: