Ricci Tensor - Mathematics & Logic - Pure Mathematics Dictionary Definition The symmetric (0,2)-tensor obtained by contracting the Riemann curvature tensor on one pair of indices, Ric(X,Y) = trace_{g}(Z -> R(Z,X)Y), which encodes averaged directional curvature information and acts on tangent vectors.
Ricci Tensor - Mathematics & Logic - Pure Mathematics Dictionary Definition The symmetric (0,2)-tensor obtained by contracting the Riemann curvature tensor on one pair of indices, Ric(X,Y) = trace_{g}(Z -> R(Z,X)Y), which encodes averaged directional curvature information and acts on tangent vectors.