Triviality problem for nil-isotropic automorphisms of non-quadratic CR-manifolds

We present a survey on the effect of triviality of nil-isotropic automorphisms of real-analytic non-quadratic Levi non-degenerate CR manifolds. As a new result we prove that any isotropic automorphism of an elliptic CR-manifold in ℂ⁴ is uniquely determined by its first order derivatives at the origin and that the dimension of the corresponding Lie group does not exceed 6. Moreover, it is shown that apart from a very special family of exceptional manifolds any isotropic automorphism is determined by the restriction of its differential at the origin to the complex tangent space.