Integration by completely integrable Pfaffian equations

Theorem
Given an involutive distribution $\mathcal{Z}=\mathcal{S}(\{Z_1,\dots ,Z_r\})$ and a cinf-structure $⟨{\omega }_1,\dots ,{\omega }_{n-r}⟩$ for $\mathcal{Z}$ we can find the integral manifolds of $\mathcal{Z}$ by solving $n-r$ completely integrable Pfaffian equations.

Remarks

• It is not needed to find the integrating factors.
• In the second-order case, it is equivalent to the $\lambda$-symmetry method of @muriel01ima1.
• Description of the cinf-structure-based method.

References:
@pancinf-sym
@pancinf-struct
@pan23integration