In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, measures how a curved space locally differs from flat space by tracking how nearby geodesics spread apart or converge.
Formally, it is a symmetric rank-two tensor obtained by taking a trace of the Riemann curvature tensor of a Riemannian or pseudo-Riemannian metric. In Riemannian geometry, the Ricci curvature in a given tangent direction may be interpreted as an average of the sectional curvatures of plan...
