The rigidity of totally nondegenerate model CR manifolds

TL;DR

This paper proves that all real analytic totally nondegenerate model CR manifolds of length three or more are rigid, confirming a long-standing conjecture that their automorphism groups are linear.

Contribution

It establishes the rigidity of these CR manifolds, confirming Valerii Beloshapka's maximum conjecture for length >= 3.

Findings

All such CR manifolds have no nonlinear automorphisms.

The transformation groups are linear.

The result applies to manifolds of length at least 3.

Abstract

In this paper, we prove that every real analytic totally nondegenerate model CR manifold of length >= 3 has rigidity. This result was actually conjectured before by Valerii Beloshapka as the so-called "maximum conjecture". It follows that the transformation Lie group of all CR automorphisms associated with each of the mentioned models does not include any nonlinear map.