= Isotropic Ricci curvature
{title2=$\operatorname{Ric}_p=c_p g_p$}
At a point of a <Riemannian manifold>, Ricci curvature is isotropic when $\operatorname{Ric}(v,v)/g(v,v)$ is independent of nonzero tangent direction. Polarization makes this equivalent to the displayed tensor identity. In dimension three, <sectional curvatures from Ricci curvature in dimension three> gives every sectional curvature at that point the value $c_p/2$. In higher dimensions isotropic Ricci curvature does not determine every two-plane curvature.
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