Word.ws English Dictionary

differential form

differential form noun: a completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.

Noun

differential form (plural differential forms)

  1. (sometimes, differential geometry) A completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.
    • The notion of differential form combines the concepts of multilinear form (itself an extension of linear form) and smooth function.
    • The choice of a Riemannian manifold - roughly speaking, a differentiable manifold whose every point has a tangent space with a defined metric - means it is possible to define a differential form over it.

differential form meaning in Tamil

differential form in Tamil

வகையீட்டு வடிவம்

Examples of differential form in a sentence

  • Now that the length of tangent vector is defined, the magnitude of a differential form is also determined.2001, Shigeyuki Morita, translated by Teruko Nagase and Katsumi Nomizu, Geometry of Differential Forms, American Mathematical Society, page...
  • In this first chapter, we discuss various versions of the Hardy-Littlewood inequality for differential forms, including the local cases, the global cases, one weight cases, and two-weight cases.2009, Ravi P. Agarwal, Shusen Ding, Craig Nolder, Inequalities for Differential Forms, Springer, page 1:

Forms of differential form

pluraldifferential forms

Origin of differential form

From early 20th century. The concept was clarified chiefly by French mathematician Élie Cartan (1869–1951). In his fundamental paper, 1899, Sur certaines expressions différentielles et le problème de Pfaff, Annales Scientifiques de l'École Normale Supérieure (3), tome 16, Cartan used the (French) term expression différentielle, and in his 1922, Leçons sur les invariants intégraux, Hermann, he used the terms exterior differential form and exterior derivative.

Words formed from differential form

Questions about differential form

What does differential form mean?
Differential form means a completely antisymmetric tensor (of order p) that is defined on a Riemannian manifold; an expression, derived by applying a formalism to said tensor, that represents an integrand over the manifold.
What is differential form in Tamil?
Differential form in Tamil is வகையீட்டு வடிவம். See Differential form meaning in Tamil.
How do you use differential form in a sentence?
Now that the length of tangent vector is defined, the magnitude of a differential form is also determined.
What part of speech is differential form?
Differential form is a noun.
What is the plural of differential form?
The plural of differential form is differential forms.

Words near differential form in the dictionary

  1. differential calculus
  2. differential diagnoses
  3. differential diagnosis
  4. differential equation
  5. differential equations
  6. differential form
  7. differential forms
  8. differential gear
  9. differential gears
  10. differential geometries
  11. differential geometry

Source and license

Adapted from Wiktionary: differential form (page history and authors); differential form (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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