= Normalized Ricci curvature
{title2=$\overline{\operatorname{Ric}}=\operatorname{Ric}/(n-1)$}
For a <Riemannian manifold> of dimension $n\geq2$, the normalized directional <Ricci curvature> averages, rather than sums, the $n-1$ <sectional curvatures> through a unit vector. Thus the <Bonnet-Myers theorem> gives $\operatorname{diam}M\leq\pi/\sqrt k$ from $\overline{\operatorname{Ric}}\geq kg$. With trace Ricci curvature the corresponding hypothesis is $\operatorname{Ric}\geq(n-1)kg$. The distinction changes positive constants but not the signs of Ricci curvature.
Back to article page
