On the Beloshapka's rigidity conjecture for real submanifolds in complex space

Abstract

A well known Conjecture due to Beloshapka asserts that all totally nondegenerate polynomial models with the length $l\ge 3$ of their Levi-Tanaka algebra are {\em rigid}, that is, any point preserving automorphism of them is completely determined by the restriction of its differential at the fixed point onto the complex tangent space. For the length $l=3$, Beloshapka's Conjecture was proved by Gammel and Kossovskiy in 2006. In this paper, we prove the Conjecture for arbitrary length $l\ge 3$. As another application of our method, we construct polynomial models of length $l\ge 3$, which are not totally nondegenerate and admit large groups of point preserving nonlinear automorphisms.

24pp, the reference [SS18] is added to article that appeared practically at the same time and that is independently proving the Main Theorem