Differential 1-form

This article defines a basic construct that makes sense on any differential manifold
View a complete list of basic constructs on differential manifolds

Definition

Symbol-free definition

A differential 1-form on a differential manifold is a section of its cotangent bundle.

We can also talk of a differential 1-form restricted to an open subset, which is a section of the restriction of the cotangent bundle to the open subset. This gives rise to the notion of the sheaf of differential 1-forms