Locally CR Spherical Three Manifolds

TL;DR

This paper discusses the existence of locally equivalent CR structures on open, orientable three-manifolds, highlighting their relation to the standard CR structure on the three-sphere.

Contribution

It establishes that every open, orientable three-manifold admits a CR structure locally equivalent to that on $S^3$, expanding understanding of CR structures in three dimensions.

Findings

All open, orientable three-manifolds have locally standard CR structures.

The standard CR structure on $S^3$ serves as a local model for these manifolds.

The result applies broadly to the class of open, orientable three-manifolds.

Abstract

Every open and orientable three manifold has a CR structure which is locally equivalent to the standard CR structure on $S^3$.