Conformality is Equivalence Relation on Set of Riemannian Metrics

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Theorem

Let $M$ be a smooth manifold.

Let $\set g$ be the set of Riemannian metrics on $M$.



Suppose $\set g$ is equipped with the conformality relation.

That is, suppose that for any pair of Riemannian metrics there is a conformal transformation.


Then conformality relation is equivalence relation.


Proof




Sources