: Mathématiques: Frobenius' theorem

geometry > differential geometry > Frobenius' theorem

topology > differential topology > Frobenius' theorem

Frobenius' theorem

In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of r vector fields mesh into coordinate grids on r-dimensional integral manifolds. The theorem is foundational in differential topology and calculus on manifolds.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Frobenius_theorem_(differential_topology))

http://data.loterre.fr/ark:/67375/PSR-L2MHCD1K-M

RDF/XML TURTLE JSON-LD Date de création 19/07/2023, dernière modification le 19/07/2023

Loterre