3-Manifolds with Positive Flat Conformal Structure

TL;DR

This paper proves that closed 3-manifolds with positive Yamabe constant and flat conformal structure are Kleinian, linking geometric properties to conformal structures.

Contribution

It establishes a new characterization of 3-manifolds with flat conformal structures based on the positivity of the Yamabe constant.

Findings

Positive Yamabe constant implies the manifold is Kleinian.

Provides a geometric classification for 3-manifolds with flat conformal structures.

Connects conformal geometry with Kleinian groups.

Abstract

In this paper, we consider a closed 3-manifold $M$ with flat conformal structure $C$. We will prove that, if the Yamabe constant of $(M, C)$ is positive, then $(M, C)$ is Kleinian.