# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1702.03213