##  [Ricci Tensor](/ricci-tensor) 

  ##  [Ricci Tensor](https://puremath.quantumdictionary.io/ricci-tensor-0) 

  

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**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.