rotorformen

Rotorformen, literally rotor forms, is a term encountered in some German-language or bilingual texts to denote a class of differential forms associated with rotational properties of fields. In this usage, a rotor form is any differential form that encodes the rotational or vorticity aspects of a vector field, typically through the exterior derivative, the Hodge star operator, and their combinations. In three dimensions, the curl of a vector field F corresponds to the Hodge dual of the exterior derivative of the 1-form α that represents F, and rotorformen are often discussed as the 2-forms dα or *dα which carry the same information as the vector curl.

Rotorformen are used to express rotational phenomena in a coordinate-free way. They enable concise descriptions of vorticity in fluids, magnetic field topology in electromagnetism, and angular momentum densities in continuous media. Their algebraic properties follow from the usual calculus of differential forms: d^2=0, and relations with the Hodge star depend on the metric.

The term is not universally standardized and may appear mainly in certain texts or courses on differential geometry, mathematical physics, or German-language literature. In broader contexts, rotor concepts are more commonly described through curls, vorticity forms, or 2-forms derived from 1-forms representing vector fields.

See also: differential forms, exterior calculus, curl, vorticity, electromagnetism.