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...

exact differential forms Complex differential form Vector-valued differential form Equivariant differential form Calculus on Manifolds Multilinear form Polynomial...

and d ν {\displaystyle d\nu } the differential of ν {\displaystyle \nu } regarded as a vector-valued differential form, and the brackets denote the metric...

In differential geometry, a Lie-algebra-valued form is a differential form with values in a Lie algebra. Such forms have important applications in the...

multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used...

connection and vector-valued differential forms. A 'naïve' attempt to define the derivative of a tensor field with respect to a vector field would be...

A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional...

derivative. A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is not tensorial because...

any differential k-form ω and any vector-valued form s. This may also be viewed as a direct inductive definition. For instance, for any vector-valued differential...

know which vectors have their directions unchanged by a given linear transformation. An eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is such...