In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...

and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α...

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section...

complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms have...

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...

shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry...

has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory...

field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional...

. More generally, any covariant tensor field – in particular any differential form – on N {\displaystyle N} may be pulled back to M {\displaystyle M}...

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...