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A new proof of Frobenius theorem and applications

Abstract

A proof of Frobenius theorem on local integrability of a given distribution on a finite or infinite dimensional manifold under weak differentiability conditions is given using holonomy methods and the curvature two form of the associated connection. The local curvature two form, which measures the non-integrability of a given distribution, is studied and a variety of applications are given. The Inverse Problem in the Calculus of Variations appears as a particular case.

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Cendra, H., Lacomba, E.A. & Verdiell, A. A new proof of Frobenius theorem and applications. Z. angew. Math. Phys. 44, 266–281 (1993). https://doi.org/10.1007/BF00914284

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Keywords

  • Manifold
  • Inverse Problem
  • Mathematical Method
  • Dimensional Manifold
  • Local Curvature