A hypersurface in \C^2 whose stability group is not determined by 2-jets

TL;DR

This paper presents a specific example of a hypersurface in complex two-space where the stability group at a point is uniquely determined by third-order derivatives but not by lower orders, revealing nuanced geometric properties.

Contribution

The paper introduces a hypersurface in \\C^2 with a stability group not fully determined by lower-order jets, highlighting complex behaviors in CR geometry.

Findings

Stability group determined by 3-jets but not by lower jets

Shared properties with the 3-sphere in \\C^2

Example of infinite type hypersurface

Abstract

We give an example of a hypersurface in \C^2 through 0 whose stability group at 0 is determined by 3-jets, but not by jets of any lesser order. We also examine some of the properties which the stability group of this infinite type hypersurface shares with the 3-sphere in \C^2.