# Real-analytic coordinates for smooth strictly pseudoconvex CR-structures

## TL;DR

This paper establishes a precise criterion for when smooth strictly pseudoconvex CR structures can be transformed into real-analytic ones, based on holomorphic extension properties of associated functions.

## Contribution

It introduces a necessary and sufficient condition involving holomorphic extension for CR-diffeomorphism to real-analytic structures, connecting jet extension properties with CR geometry.

## Key findings

- Characterizes CR-diffeomorphism to real-analytic structures via extension conditions
- Links jet extension properties to Fefferman type determinants
- Provides a new criterion for analyticity in CR-structures

## Abstract

For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically associated function expressing $2$-jets of the formal Segre varieties in terms of their $1$-jets. We also express this condition in equivalent terms for a Fefferman type determinant