##  [Symplectic Manifold](/symplectic-manifold) 

  ##  [Symplectic Manifold](https://natural.quantumdictionary.io/symplectic-manifold-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A smooth even-dimensional manifold equipped with a closed, nondegenerate differential 2-form (the symplectic form) that provides a bilinear pairing on each tangent space and underlies Hamiltonian mechanics.