Symplectic form

This article defines a property that can be evaluated to true/false for a differential form (of any order)

Definition

A differential 2-form is said to be a symplectic form if it satisfies the following:

• It is a closed form
• On each tangent space, it is alternating and nondegenerate

Equivalently, a symplectic form is the form associated with a symplectic manifold.

Further information: symplectic manifold

Relation with other properties

Stronger properties

• Exact symplectic form

Weaker properties

• Closed form