differential form

Meaning

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.

Related

Narrower meaning words

• Pfaffian form

Origin

• 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.