Orbits of Families of Vector Fields and Integrability of Distributions
Orbits of Families of Vector Fields and Integrability of Distributions
Let $D$ be an arbitrary set of ${C^\infty }$ vector fields on the ${C^\infty }$ manifold $M$. It is shown that the orbits of $D$ are ${C^\infty }$ submanifolds of $M$, and that, moreover, they are the maximal integral submanifolds of a certain ${C^\infty }$ distribution ${P_D}$. (In general, the …