Triviality problem for nil-isotropic automorphisms on non-quadratic CR-manifolds (Q2726219)

Let \(M\) be a real analytic submanifold of codimension \(k\) in \(\mathbb{C}^{n+k}\) containing the origin 0.NEWLINENEWLINENEWLINEAfter recalling the notion of Levi non-degeneracy for \(M\), the authors first define the group \(\text{Aut}_{0,\text{id}}M\) of nil-isotropic automorphisms, which is a subgroup of the local isotropy group \(\text{Aut}_0M\) at \(0\). Next, recalling the notion of elliptic CR-manifold \(M\), the authors prove that for any real-analytic non-quadratic elliptic CR-manifold \(M\) the group \(\text{Aut } M_{0,\text{id}} M\simeq\text{id}\) or \(\mathbb{C}\).NEWLINENEWLINENEWLINEThe authors next survey on the effect of triviality of nil-isotropic automorphisms of real-analytic non-quadratic Levi non-degenerate CR-manifolds, elliptic and hyperbolic CR-manifolds of codimension 2 in \(\mathbb{C}^4\) in the works of \textit{V. K. Beloshapka} [Izv. Akad. Nauk SSSR, Ser. Mat. 43, 243-266 (1979; Zbl 0412.58010)], \textit{A. V. Loboda} [ibid. 45, 620-645 (1981; Zbl 0473.32016)], \textit{G. Schmalz} [Math. Nachr. 196, 189-229 (1998; Zbl 0933.32050)], and others.