In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...
66 KB (9,950 words) - 14:18, 10 February 2024
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...
13 KB (2,228 words) - 18:37, 5 May 2024
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...
5 KB (752 words) - 03:33, 19 July 2024
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...
13 KB (2,253 words) - 22:50, 21 September 2021
complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms have...
9 KB (1,413 words) - 02:38, 27 April 2024
shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry...
46 KB (5,912 words) - 08:09, 21 August 2024
In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced...
26 KB (4,378 words) - 08:13, 20 September 2023
Hodge theory (redirect from Harmonic differential form)
has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory...
28 KB (4,309 words) - 16:21, 17 August 2024
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...
29 KB (3,628 words) - 15:16, 20 August 2024
Gauss's law (section Differential form)
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...
27 KB (3,810 words) - 23:23, 7 August 2024