Explicit construction of stationary discs and its consequences for nondegenerate quadrics

TL;DR

The paper explicitly constructs stationary discs attached to nondegenerate quadrics in complex space and explores conditions for their unique determination by jets, advancing understanding of CR automorphisms.

Contribution

It provides an explicit construction of stationary discs for nondegenerate quadrics and establishes conditions for their unique jet determination, aiding CR automorphism analysis.

Findings

Explicit construction of stationary discs for nondegenerate quadrics

Necessary condition for unique 1-jet determination of stationary discs

Implication for 2-jet determination of CR automorphisms

Abstract

We give an explicit construction of a key family of stationary discs attached to a nondegenerate model quadric in $\mathbb{C}^N$ and derive a necessary condition for which (each lift) of those stationary discs is uniquely determined by its $1$-jet at a given point via a local diffeomorphism. This unique $1$-jet determination is a crucial step to deduce $2$-jet determination for CR automorphisms of generic real submanifolds in $\mathbb{C}^N$.