 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