Math 6510 • Differentiable Manifolds

\begin{enumerate}
\item State the Frobenius integrability theorem.
\item Show that the plane field in \(\mathbb{R}^3\) spanned by the vector fields
\[
  X=\frac{\partial}{\partial x}+z\frac{\partial}{\partial y}
  \qquad\text{and}\qquad
  Y=\frac{\partial}{\partial z}
\]
is not integrable on any nonempty open subset of \(\mathbb{R}^3\).
\end{enumerate}