On the Integrability of Pfaffian Forms on \mathbb Rⁿ

2021/10/15 by Júnior, Pedro F. da Silva
#34A99 #58A99 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2110.08337

Abstract

This paper details the lesser known conditions on \mathbb Rⁿ for the integrability of pfaffian forms, or 1-forms. Emphasis is given to locality of these conditions, and proofs in some additional detail are provided for theorems due to Clairaut and Carathéodory. Considering the importance of the integrability of pfaffian forms, in particular in mathematical-physics, this paper shows that: there is a hidden content in Carathéodory's theorem in the direction of a global integrability.

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