= Conformal group
{title2=$\operatorname{Conf}(M,g)$}
The <conformal group> of a metric manifold consists of <diffeomorphisms> $f$ with $f^*g=\Omega^2g$ for a positive function $\Omega$. Its infinitesimal generators are <Conformal Killing vector fields>. The choice of manifold matters: in flat Euclidean dimension greater than two, <special conformal transformations> can be regular on the <conformal compactification of Euclidean space> while having finite poles in the uncompactified space.
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