##  [Geodesic Deviation](/geodesic-deviation) 

  ##  [Geodesic Deviation](https://puremath.quantumdictionary.io/geodesic-deviation-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Second-order linear mechanism describing how an infinitesimal separation vector between nearby geodesics evolves along a reference geodesic; concretely, a Jacobi field J satisfies the Jacobi (geodesic deviation) equation which couples the second covariant derivative of J to the curvature operator acting on J and the geodesic tangent.