Normal form for pseudo-Einstein contact forms and intrinsic CR normal coordinates

TL;DR

This paper develops a normal form for pseudo-Einstein contact forms in CR geometry and constructs intrinsic CR normal coordinates using parabolic normal coordinates, enhancing the understanding of CR structures.

Contribution

It introduces a new normal form for pseudo-Einstein contact forms and constructs intrinsic CR normal coordinates based on parabolic normal coordinates.

Findings

Normal form for pseudo-Einstein contact forms established

Construction of intrinsic CR normal coordinates parametrized by the structure group

Application of Jerison and Lee's parabolic normal coordinates method

Abstract

We give a normal form for pseudo-Einstein contact forms and apply it to construct intrinsic CR normal coordinates parametrized by the structure group of CR geometry. The proof is based on the construction of parabolic normal coordinates by Jerison and Lee.