# Curvature tensor of a conformally flat manifold

Let $M$ be a manifold of dimension $n>3$ and $g$ a Riemannian metric on $M$ which is conformally equivalent to a flat one. Are there formulas (different from $R(u,v)w=\nabla_u\nabla_vw-\nabla_v\nabla_uw-\nabla_{[u,v]}w$) that allow to compute easily the curvature tensor of a conformally flat manifold such as $(M,g)$?