Conformally equivalent metrics
Two Riemannian metrics on a differential manifold are termed conformally equivalent if one of them can be obtained as a scalar function times the other one. In other words, at each point, one metric is simply a constant times the other metric (the constant may vary from point to point).
Definition with symbols
Let and be two Riemannian metrics on a differential manifold . Then we say that is conformally equivalent to if there is a scalar function such that for any , and tangent vectors :