Talk:Conformality is Equivalence Relation on Set of Riemannian Metrics

Notation
The set $\set {g}$ is supposed to denote a collection of all Riemannian metrics which are admissible to $M$. The precise condtions come from the topology and differentiable structure of $M$. Then we are supposed to pick a subset of these metrics which in addition are related by conformal transformations. Then the conformal transformation as a relation on this subset of metrics is an equivalence relation. Maybe what we need is a set of all Riemannian metrics on $M$ like $S = \set {g : g \text { is a Riemannian metric on } M}$, and then define the conformal subset $C \subseteq S$ on which the equivalence relation will be proved?--Julius (talk) 12:10, 2 June 2023 (UTC)


 * The notation needs to be explained properly, because it makes no mathematical sense according to what we have on.