Let $(M,g)$ be a Riemannian manifold, and $x\in M$ be a fixed point. **Q** Can we find a conformal transformation such that near $x$ we can write $e^{2u}g$ as $(dx^1)^2+...+(dx^n)^2$? Since the question is local, we can replace $M$ with $\mathbb R^n$. (PS: Any reference is welcome.)