Vector-valued differential form

In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms (a connection form is an example of such a form.) == Definition == Let M be a smooth manifold and E → M be a smooth vector bundle over M. We denote the space of smooth sections of a bundle E by Γ(E).

Source: Wikipedia — Vector-valued differential form (CC BY-SA 4.0)

Vector-valued differential form

In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms (a connection form is an example of such a form.) == Definition == Let M be a smooth manifold and E → M be a smooth vector bundle over M. We denote the space of smooth sections of a bundle E by Γ(E).

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Source: Wikipedia "Vector-valued differential form" · CC BY-SA 4.0

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