• In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...
    66 KB (9,469 words) - 14:18, 10 February 2024
  • In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold M{\displaystyle...
    5 KB (742 words) - 15:14, 14 November 2022
  • 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 (2,087 words) - 10:21, 27 December 2023
  • 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 (1,330 words) - 11:05, 5 January 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 (2,160 words) - 22:50, 21 September 2021
  • Thumbnail for Differential geometry
    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 (5,873 words) - 21:09, 11 February 2024
  • 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 (4,095 words) - 06:45, 19 January 2024
  • ^{*}}. More generally, any covariant tensor field – in particular any differential form – on N{\displaystyle N} may be pulled back to M{\displaystyle M} using...
    13 KB (2,184 words) - 23:03, 28 August 2023
  • Thumbnail for Gauss's law
    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 (3,562 words) - 03:42, 8 February 2024
  • In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal...
    26 KB (3,740 words) - 04:13, 24 February 2024