One-form

Definition

In differential geometry, a one-form on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the tangent space. Let be an open subset of and . Then defines a one-form . is a covector.

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