Intrinsic regular surfaces of low codimension in Heisenberg groups

In this paper we study intrinsic regular submanifolds of \(\mathbf{H}^n\) low codimension in relation with the regularity their parametrization. We extend some results proved for \(\mathbf{H}\)-regular surfaces 1 to \(k\), \(1 \leq k n\). characterize uniformly differentiable functions, \(\phi\), acting between two complementary subgroups Heisenberg group \(\mathbf{H}^n\), target space horizontal dimension terms Euclidean components respect a family non linear vector fields \(\nabla^{\phi_j}\). Moreover, show how area graph \(\phi\) can be computed matrix representing differential \(\phi\).