##  [Ricci Curvature](/ricci-curvature) 

  ##  [Ricci Curvature](https://natural.quantumdictionary.io/ricci-curvature-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A symmetric 2-tensor on a Riemannian manifold obtained by contracting the Riemann curvature tensor; it measures, in an averaged sense over directions, how geodesic volumes and the Laplacian's behavior deviate from the flat case.