= Conformal class of a Riemannian metric
{title2=$[g]=\{e^{2\varphi}g:\varphi\in C^\infty(M,\mathbb R)\}$}
= Conformal class
{synonym}
Two <Riemannian metrics> lie in the same conformal class when one is a positive smooth scalar multiple of the other. They measure the same <angles>, while <lengths> may change from point to point. On an oriented <Riemannian surface>, rotation of each <tangent plane> through $\pi/2$ determines a <complex structure> which depends only on this conformal class.
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