One form

One-forms are widely used in differential geometry. Their duality with vector fields makes them suited to encode algebraic conditions on vector fields, and conditions such as integrability of systems of vector fields are often simpler to formulate in terms of one-forms, together with the exterior derivative. One forms are also used in differential geometry to encode other tensors, such as the metric tensor; a selected basis of one-forms is called a coframe, and special coframes are widely used throughout Riemannian and pseudo-Riemannian geometry.