Symplectic Structure on a Manifold

We have introduced a symplectic linear structure in the tangent space to 

Definition 1.2.5 A smooth even-dimensional manifold M is called symplectic if on this manifold is given an exterior differential 2-form (that is,form of degree 2) 

1) This form is nondegeneratCf that is, the matrix of its coefficients n(x) = 

2) This form is closed, that is, its exterior differential is equal to zero du) = 0. Such a form is called a symplectic structure on M.  

Here a i. X2n are local regular coordinates on At each point x G such a 2-form apparently determines the linear symplectic structure 

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A similar assertion is valid in a multidimensional case as well. Let a be a symplectic structure on a manifold Then the nth exterior degree of the 2-... 

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