On a remarkable formula of Jerison and Lee in CR geometry

TL;DR

This paper extends Jerison and Lee's formula for classifying constant scalar curvature pseudohermitian structures from the sphere to Einstein pseudohermitian manifolds, leading to a broader uniqueness result.

Contribution

It generalizes Jerison and Lee's classification formula to Einstein pseudohermitian manifolds and proves a new uniqueness theorem.

Findings

Formula valid in wider Einstein pseudohermitian context

Established a new uniqueness result for these structures

Broadened understanding of scalar curvature classification

Abstract

We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jerison and Lee.