A Counterexample to the $2$-jet determination Chern-Moser Theorem in higher codimension

TL;DR

This paper presents a specific example of a high-codimension CR manifold that challenges the general applicability of the Chern-Moser theorem for 2-jet determination, highlighting limitations in existing classification methods.

Contribution

It constructs a counterexample in higher codimension showing the failure of 2-jet determination by the Chern-Moser theorem.

Findings

Existence of a quadratic CR manifold with nontrivial automorphisms

Counterexample in codimension 5 in ^9

Automorphisms with degree 3 polynomial coefficients

Abstract

One constructs an example of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $3.$