# Conformal structure on a differential manifold

## Contents

## Definition

### Given data

A connected differential manifold .

### Definition part

A **conformal structure** on associates to a class of conformally equivalent metrics, viz it associates to a Riemannian metric that is *loose* upto conformal equivalence.

Thus, every Riemannian metric gives a conformal structure and every conformal structure arises from a Riemannian metric, but different Riemannian metrics may give rise to the same conformal structure.

## Facts

### Volume-normalization of a conformal structure

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