Conformal structure
= Conformal structure
{title2=$[g]=\{e^{2u}g:u\in C^\infty(M)\}$}
An equivalence class of <Riemannian metrics> under multiplication by positive smooth functions. Such rescalings preserve angles. On an oriented smooth surface, a conformal structure is equivalent to a <complex structure>, with local holomorphic coordinates in which its metrics are positive multiples of $dx^2+dy^2$.