A characterization of homogeneous three-dimensional CR manifolds

TL;DR

This paper characterizes homogeneous three-dimensional CR manifolds, including Rossi spheres, as critical points of an energy functional based on Webster curvature and torsion, providing a new geometric perspective.

Contribution

It introduces a novel characterization of homogeneous 3D CR manifolds via an energy functional involving Webster curvature and torsion.

Findings

Homogeneous 3D CR manifolds are critical points of the specified energy functional.

Rossi spheres are explicitly characterized within this framework.

The approach links geometric invariants to variational principles.

Abstract

We characterize homogeneous three-dimensional CR manifolds, in particular Rossi spheres, as critical points of a certain energy functional that depends on the Webster curvature and torsion of the pseudohermitian structure.