In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold ${\displaystyle M}$ is a smooth mapping of the total space of the tangent bundle of ${\displaystyle M}$ to ${\displaystyle \mathbb {R} }$ whose restriction to each fibre is a linear functional on the tangent space. Symbolically,

Often one-forms are described locally, particularly in local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates: