Almost symplectic manifold

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This article defines a differential manifold with the following additional structure -- the structure group is reduced to: symplectic group

Definition

An almost symplectic manifold is the following data:

  1. A differential manifold M of dimension n = 2m
  2. A reduction of the structure group of TM to the symplectic group, or equivalently, an association of an alternating nondegenerate bilinear form to the tangent space at every point, in a smooth way.

The second datum is termed an almost symplectic structure on the manifold.