1-form

Let be a -manifold. A 1-form or covector field is something which eats vector fields and spits out scalar fields in a linear fashion. #m/def/geo/diff In more precise terms, a 1-form is a -module homomorphism

As a section

The above definition is equivalent to a -section of the cotangent bundle. As a special case of Differential form, we denote the set of 1-forms on as

At a point, each 1-form restricts to an -linear form on the tangent space, i.e. a cotangent vector.

Proof of equivalence

#missing/proof

#state/develop | #lang/en | #SemBr