Infinitesimal automorphisms of quadrics and second jet determination for CR mappings

TL;DR

This paper proves finite jet determination results for CR mappings of Levi nondegenerate manifolds, extending known results from real analytic to smooth cases, by analyzing infinitesimal automorphisms of quadrics.

Contribution

It establishes finite jet determination for smooth Levi nondegenerate CR manifolds using automorphism algebra finite dimensionality, generalizing prior real analytic results.

Findings

Finite jet determination holds for smooth Levi nondegenerate CR manifolds.

A new 2-jet determination result is proven.

Automorphism algebra finite dimensionality underpins the main results.

Abstract

We consider a problem whether a CR mapping of a generic manifold in complex space is uniquely determined by its finite jet at a point, which is referred to as finite jet determination. We derive the finite jet determination for CR mappings of smooth Levi nondegenerate manifolds of arbitrary codimension from the finite dimensionality of the algebras of infinitesimal automorphisms of the corresponding quadrics. Previously, this implication was known for real analytic manifolds. We prove a new 2-jet determination result that covers most affirmative results on this matter obtained so far.