##  [Toponogov Comparison Theorem](/toponogov-comparison-theorem) 

  ##  [Toponogov Comparison Theorem](https://puremath.quantumdictionary.io/toponogov-comparison-theorem-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A comparison theorem in Riemannian geometry that relates geodesic triangles in a complete Riemannian manifold to triangles in a model space of constant sectional curvature, given a lower bound on the manifold's sectional curvature.