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A conformally flat metric is locally $g={\Omega }^2\eta$, where $\Omega >0$ is a smooth conformal factor and $\eta$ is a flat metric tensor. Its domain is a conformally flat manifold. The conformal factor preserves null cones and unparametrized null geodesics, but can change curvature.^[ref] For example, $g=a(\eta {)}^2(-d{\eta }^2+d{\mathbf{x}}^2)$ has Ricci scalar $R=6a^{\prime \prime }/a^3$ in the usual general relativity curvature convention, so conformal flatness need not mean flatness.