Let $n\in\mathbb N$ with $n\ge 2$, and let $K\in\mathbb R$. Let $(M,g)$ be a connected complete smooth $n$-dimensional Riemannian manifold, let $d_g:M\times M\to[0,\infty)$ be its Riemannian distance, and let $\operatorname{vol}_g$ be its Riemannian volume measure. Then the metric-measure space $(M,d_g,\operatorname{vol}_g)$ satisfies the Lott--Sturm--Villani curvature-dimension condition $CD(K,n)$ with distortion coefficients $\tau_{K,n}^{(t)}$ if and only if

\begin{align*} \operatorname{Ric}_g(v,v)\ge K g_p(v,v) \end{align*}

for every $p\in M$ and every $v\in T_pM$.