| Popis: |
Given a system of smooth 1-forms µ = (µ 1 ;:::;µ s ) on a smooth manifold M m , we give a necessary and su-cient condition for M to be foliated by integral manifolds of dimension n, np := m i s; and construct an integrable supersystem (µ;·) by flnding additional 1-forms · = (· 1 ;:::;· pin ): We also give a necessary and su-cient condition for M to be foliated by reduced submanifolds of dimension n, n ‚ p; and con- struct an integrable subsystem (d‰ 1 ;:::;d‰ min ) by flnding a system of flrst integrals ‰ = (‰ 1 ;:::;‰ min ): The special case n = p is the Frobenius theorem on involutivity. |
