##  [Exponential Map](/exponential-map) 

  ##  [Exponential Map](https://puremath.quantumdictionary.io/exponential-map-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The map exp_p from the tangent space T_pM at a point p of a (typically Riemannian) manifold M to M that sends a tangent vector v to the endpoint γ_v(1) of the geodesic γ_v with initial velocity v, defined on the maximal domain where those geodesics exist.