# Conformally equivalent metrics

Let $g_1$ and $g_2$ be two Riemannian metrics on a differential manifold $M$. Then we say that $g_1$ is conformally equivalent to $g_2$ if there is a scalar function $f:M \to \mathbb{R}^*$ such that for any $p \in M$, and tangent vectors $v,w \in T_pM$:
$g_1(v,w) = f(p)g_2(v,w)$